Theoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, predicting physical phenomena through a "physical theory". There are three types of theories in physics; mainstream theories, proposed theories and fringe theories.
Some physical theories are backed by observation, whereas others are not. A physical theory is a model of physical events and cannot be proved from basic axioms. A physical theory is different from a mathematical theorem. Physical theories model reality and are a statement of what has been observed, and provide predictions of new observations.
Physical theories can become accepted if they are able to make correct predictions and avoid incorrect ones. Physical theories which are simpler tend to be accepted over theories which are complex. Physical theories are more likely to be accepted if they connect a wide range of phenonomena. The process of testing a physical theory is part of the scientific method.
Theoretical physics is just one important part of physics; the other part is experimental physics. The difference between theoretical physics and mathematical physics is that mathematical physics finds the mathematical rigor required in mathematics to be more important than the contact with experiments and observations.
A list of theoretical physicists can be found here.
