The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.
In common usage, people often use the word theory to signify a conjecture, an opinion, or a speculation. In this usage, a theory is not necessarily based on facts; in other words, it is not required to be consistent with true descriptions of reality. True descriptions of reality are more reflectively understood as statements which would be true independently of what people think about them. In this usage, the word is synonymous with hypothesis. This common usage of theory leads to the common but misguided statement "It's not a fact, it's only a theory."
In science, a theory is a mathematical or logical explanation, or a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation. It follows from this that for scientists "theory" and "fact" do not necessarily stand in opposition. For example, it is a fact that an apple dropped on earth has been observed to fall towards the center of the planet, and the theories commonly used to describe and explain this behaviour are Newton's theory of universal gravitation (see also gravitation), and general relativity.

Etymology
In scientific usage, a theory does not mean an unsubstantiated guess or hunch, as it can in everyday speech. A theory is a logically self-consistent model or framework for describing the behavior of a related set of natural or social phenomena. It originates from or is supported by experimental evidence (see scientific method). In this sense, a theory is a systematic and formalized expression of all previous observations which is predictive, logical and testable. In principle, scientific theories are always tentative, and subject to corrections or inclusion in a yet wider theory. Commonly, a large number of more specific hypotheses may be logically bound together by just one or two theories. As a general rule for use of the term, theories tend to deal with much broader sets of universals than do hypotheses, which ordinarily deal with much more specific sets of phenomena or specific applications of a theory.

Science
The term theoretical is sometimes used to describe a result which is predicted by theory but has not yet been adequately tested by observation or experiment. It is not uncommon for a theory to produce predictions which are later confirmed or proven incorrect by experiment.

The term theoretical
In physics the term theory is generally used for a mathematical framework — derived from a small set of basic principles (usually symmetries - like equality of locations in space or in time, or identity of electrons, etc) — which is capable of producing experimental predictions for a given category of physical systems. A good example is electromagnetic theory, which encompasses the results which can be derived from gauge symmetry (sometimes called gauge invariance) in a form of a few equations called Maxwell's equations. Another name for this theory is classical electromagnetism. Note that the specific theoretical aspects of classical electromagnetic theory, which have been consistently and successfully replicated for well over a century, are termed "laws of electromagnetism", reflecting the fact that they are today taken as granted. Within electromagnetic theory generally, there are numerous hypotheses about how electromagnetism applies to specific situations. Many of these hypotheses are already considered to be adequately tested, with new ones always in the making and perhaps untested as yet.

In physics
The term theory is occasionally stretched to refer to theoretical speculation which is currently unverifiable. Examples are string theory and various theories of everything.

Currently unverifiable theories

Theories as "models"
Theories are constructed in order to explain, predict and master phenomena (e.g. inanimate things, events, or the behaviour of animals). In many instances we are constructing models of reality. A theory makes generalizations about observations and consists of an interrelated, coherent set of ideas and models.

Purpose
According to Stephen Hawking in A Brief History of Time, "a theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model which contains only a few arbitrary elements, and it must make definite predictions about the results of future observations". He goes on to state, "any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single repeatable observation which disagrees with the predictions of the theory".

Description and prediction
This is a view shared by Isaac Asimov. In Understanding Physics, Asimov spoke of theories as "arguments" where one deduces a "scheme" or model. Arguments or theories always begin with some premises - "arbitrary elements" as Hawking calls them (see above), which are here described as "assumptions". An assumption according to Asimov is "something accepted without proof, and it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either (If there were, it would no longer be an assumption). It is better to consider assumptions as either useful or useless, depending on whether deductions made from them corresponded to reality.... On the other hand, it seems obvious that assumptions are the weak points in any argument, as they have to be accepted on faith in a philosophy of science that prides itself on its rationalism. Since we must start somewhere, we must have assumptions, but at least let us have as few assumptions as possible." (See Occam's Razor)

Assumptions to formulate a theory

Examples
As an example of the use of assumptions to formulate a theory, consider how Albert Einstein put forth his Special Theory of Relativity. He took two phenomena which had been observed — that the "addition of velocities" is valid (Galilean transformation), and that light did not appear to have an "addition of velocities" (Michelson-Morley experiment). He assumed both observations to be correct, and formulated his theory, based on these assumptions, by simply altering the Galilean transformation to accommodate the lack of addition of velocities with regard to the speed of light. The model created in his theory is, therefore, based on the assumption that light maintains a constant velocity (or more precisely: the speed of light is a constant).

Special Theory of Relativity
An example of how theories are models can be seen from theories on the planetary system. The Greeks formulated theories which were recorded by the astronomer Ptolemy. In Ptolemy's planetary model, the earth was at the center, the planets and the sun made circular orbits around the earth, and the stars were on a sphere outside of the orbits of the planet and the earth. Retrograde motion of the planets was explained by smaller circular orbits of individual planets. This could be illustrated as a model, and could even be built into a literal model. Mathematical calculations could be made which predicted, to a great degree of accuracy, where the planets would be. His model of the planetary system survived for over 1500 years until the time of Copernicus. So one can see that a theory is a model of reality, one which explains certain scientific facts; yet the theory may not be a true picture of reality. Another, more accurate, theory can later replace the previous model, as when the Copernican theory replaced the Ptolemaic theory. Or a new theory can modify an older theory as when Einstein's theories of relativity modified Newtonian mechanics (which is still used for designing bridges and gasoline engines).

Ptolemy
Central to the nature of models, from general models to scale models, is the employment of representation (literally, "re-presentation") to describe particular aspects of a phenomenon or the manner of interaction among a set of phenomena. For instance, a scale model of a house or of a solar system is clearly not an actual house or an actual solar system; the aspects of an actual house or an actual solar system represented in a scale model are, only in certain limited ways, representative of the actual entity. In most ways that matter, the scale model of a house is not a house. Several commentators (e.g., Reese & Overton 1970; Lerner, 1998; Lerner & Teti, 2005, in the context of modeling human behavior) have stated that the important difference between theories and models is that the first is explanatory as well as descriptive, while the second is only descriptive (although still predictive in a more limited sense). General models and theories, according to philosopher Stephen Pepper (1948) - who also distinguishes between theories and models - are predicated on a "root" metaphor which constrains how scientists theorize and model a phenomenon and thus arrive at testable hypotheses.
In engineering practice, a distinction is made between "mathematical models" and "physical models".

Differences between theory and model
The difference between science and unscientific nonsense was well caught in Wolfgang Pauli's famous comment on a paper he was shown: "This isn't right. It's not even wrong".

Characteristics
The defining characteristic of a scientific theory is that it makes falsifiable or testable predictions about things not yet observed. The relevance, and specificity of those predictions determine how (potentially) useful the theory is. A would-be theory which makes no predictions which can be observed is not a useful theory. Predictions which are not sufficiently specific to be tested are similarly not useful. In both cases, the term 'theory' is inapplicable.
In practice a body of descriptions of knowledge is usually only called a theory once it has a minimum empirical basis. That is, it:

is consistent with pre-existing theory to the extent that the pre-existing theory was experimentally verified, though it will often show pre-existing theory to be wrong in an exact sense, and
is supported by many strands of evidence rather than a single foundation, ensuring that it is probably a good approximation, if not totally correct. Essential criteria
Additionally, a theory is generally only taken seriously if it:
This is true of such established theories as special and general relativity, quantum mechanics, plate tectonics, evolution, etc. Theories considered scientific meet at least most, but ideally all, of these extra criteria.
Theories do not have to be perfectly accurate to be scientifically useful. The predictions made by Classical mechanics are known to be inaccurate, but they are sufficiently good approximations in most circumstances that they are still very useful and widely used in place of more accurate but mathematically difficult theories.

is tentative, correctable and dynamic, in allowing for changes to be made as new data is discovered, rather than asserting certainty, and
is the most parsimonious explanation, sparing in proposed entities or explanations, commonly referred to as passing the Occam's razor test. Non-essential criteria
Sometimes it happens that two theories are found to make exactly the same predictions. In this case, they are indistinguishable, and the choice between them reduces to which is the more convenient.

Criterion for scientific status
In mathematics, the word theory is used informally to refer to certain distinct bodies of knowledge about mathematics. This knowledge consists of axioms, definitions, theorems and computational techniques, all related in some way by tradition or practice. Examples include group theory, set theory, Lebesgue integration theory and field theory.
The term theory also has a precise technical usage in mathematics, particularly in mathematical logic and model theory. A theory in this sense is a set of statements in a formal language, which is closed upon application of certain procedures called rules of inference. A special case of this, an axiomatic theory, consists of axioms (or axiom schemata) and rules of inference. A theorem is a statement which can be derived from those axioms by application of these rules of inference. Theories used in applications are abstractions of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include arithmetic (abstracting concepts of number), geometry (concepts of space), and probability (concepts of randomness and likelihood).
Gödel's incompleteness theorem shows that no consistent, recursively enumerable theory (that is, one whose theorems form a recursively enumerable set) in which the concept of natural numbers can be expressed, can include all true statements about them. As a result, some domains of knowledge cannot be formalized, accurately and completely, as mathematical theories. (Here, formalizing accurately and completely means that all true propositions – and only true propositions – are derivable within the mathematical system.) This limitation, however, in no way precludes the construction of mathematical theories which formalize large bodies of scientific knowledge.

Mathematics
Theories exist not only in the so-called hard sciences, but in all fields of academic study, from philosophy to music to literature.
In the humanities, theory is often used as an abbreviation for critical theory or literary theory.

Other fields

Astronomy: Big Bang Theory
Biology: Cell theory — Evolution
Chemistry: Atomic theory — Kinetic theory of gases
Climatology: Theory of Global Climate Change (due to anthropogenic activity)
Computer science: Algorithmic information theory — Computation theory
Economics: Decision theory
Education: Constructivist theory — Critical pedagogy theory — Education theory — Emotional education theory — Multiple intelligence theory — Progressive education theory
Engineering: Circuit theory — Control theory — Signal theory — Systems theory
Film: Film Theory
Games: Game theory — Rational choice theory
Geology: Plate tectonics
Humanities: Critical theory
Literature: Literary theory
Mathematics: Catastrophe theory — Category theory — Chaos theory — Graph theory — Knot theory — Number theory — Probability theory — Set theory
Music: Music theory
Philosophy: Proof theory — Speculative reason — Theory of truth — Type theory — Value theory — Virtue theory
Physics: Acoustic theory — Antenna theory — General relativity — Special relativity — Theory of relativity — Quantum field theory
Planetary science: Giant impact theory
Visual Art: Aesthetics — Art Educational theory — Architecture — Composition — Anatomy — Colour_theory — Perspective — Visual_perception — Geometry — Manifolds
Sociology: Sociological theory — Social theory — Critical theory
Statistics : Extreme value theory
Theatre : Theory relating to theatrical performance.
Other: Obsolete scientific theories — Phlogiston theory Scientific laws