Theoretical chemistry tries to explain data from chemistry experiments. It uses mathematics and computational analysis. Theoretical chemistry predicts what happens when atoms combine to form molecules. It also predicts chemical properties (characteristics) of molecules. An important part of theoretical chemistry is quantum chemistry.

Overview
Theoretical chemists use a wide range of tools. These tools include analytical models (for example, LCAO-MOs to approximate the behaviors of electrons in molecules) and computational and numerical simulations.

Theorists in chemistry create theoretical models. Then, they find things that experimental chemists can measure from those models. This helps chemists to look for data that can prove a model not true. The data helps to chose between several different or opposite models.

Theorists also try to generate or modify models to fit any new data, If the data can not fit the model, chemists try to make the smallest change to the model to fit the data. In some cases, chemists throw out a model if a lot of data will not fit, over time.

Theoretical chemistry uses physics to explain or predict chemical observations. In recent years, it has been mainly about quantum chemistry (the application of quantum mechanics to problems in chemistry). The main parts of theoretical chemistry are electronic structure, dynamics, and statistical mechanics.

All of these areas are used in the process of predicting chemical reactivities.  Other less central research areas include the mathematical description of bulk chemistry in various phases.  Theoretical chemists want to explain chemical kinetics (the pathway that molecules combine).

Scientists call a lot of this work "computational chemistry". Computational chemistry usually uses theoretical chemistry to work on industrial and practical problems. Examples of computational chemistry are projects to approximate chemical measurements such as certain types of post Hartree-Fock, Density Functional Theory, semiempirical methods (such as PM3) or force field methods.  Some chemical theorists use statistical mechanics to create a link between the microscopic phenomena of the quantum world and the macroscopic bulk properties of systems.

Major areas of theoretical chemistry 
Quantum chemistry The application of quantum mechanics to chemistry
Computational chemistry The application of computer codes to chemistry
Molecular modelling Methods for modelling molecular structures without necessarily referring to quantum mechanics.  Examples are molecular docking, protein-protein docking, drug design, combinatorial chemistry.
Molecular dynamics Application of classical mechanics for simulating the movement of the nuclei of an assembly of atoms and molecules.
Molecular mechanics Modelling of the intra- and inter-molecular interaction potential energy surfaces via a sum of interaction forces.
Mathematical chemistry Discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics.
Theoretical chemical kinetics Theoretical study of the dynamical systems associated with reactive chemicals and their corresponding differential equations.
Cheminformatics (also known as chemoinformatics) The use of computer and informational techniques, applied to a range of problems in the field of chemistry.

Related pages

Historically, researchers use theoretical chemistry to study:
Atomic physics: electrons and atomic nuclei.
Molecular physics:  the electrons surrounding the molecular nuclei and of movement of the nuclei.  This term usually refers to the study of molecules made of a few atoms in the gas phase. But some consider that molecular physics is also the study of bulk properties of chemicals in terms of molecules.
Physical chemistry and chemical physics: using physical methods like laser techniques, scanning tunneling microscope, etc. The formal distinction between both fields is that physical chemistry is a branch of chemistry while chemical physics is a branch of physics.  This is not a clear difference.
Many-body theory: the effects which appear in systems with large number of constituents. It is based on quantum physics – mostly second quantization formalism – and quantum electrodynamics.

More reading 
 Attila Szabo and Neil S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications; New Ed edition (1996) , 
 Robert G. Parr and Weitao Yang, Density-Functional Theory of Atoms and Molecules, Oxford Science Publications; first published in 1989; , 

 
Branches of chemistry