This article gives an overview of modem electronic structure theory, which is the development of approximate quantum mechanical methods for calculating the ground and excited electronic states of molecules. A series of seven topics are discussed which have contributed to the present state of the field and that illustrate in a general way some of the essential physical models and approximations that underpin electronic structure calculations. These topics begin from the definition of theoretical model chemistries and the treatment of electron correlation by wave function-based techniques and density functional theory, for both molecular energies and a range of molecular properties. Beyond these main theoretical issues, questions of chemical interpretation, computational algorithms, and the modeling of surrounding environment are also discussed. Collectively these topics define many of the classes of chemical problems which can be reliably and feasibly solved by such calculations at present, and conversely they also serve to define a number of unresolved challenges for the future.