The purpose of this chapter is to review the theories of molecular structure and property relations, to discuss computational methods for prediction of molecular structure and properties, and to discuss some of the properties that can be predicted by computations. Quantum mechanics is the foundation of molecular structure and properties. The position and energy of the electrons around a molecule are determined by solving the Schrödinger equation for a given set of positions of the nuclei of the atoms. There is a lot of powerful and effective computer software that can be used to calculate many of the properties of an isolated single molecule, especially at zero absolute temperature. The starting point is the construction of the sketch of a molecule by connecting atoms with the appropriate bonds. This qualitative sketch does not need accurate values for the bond lengths and angles. To set up the computation, the investigator specifies one of three computation methods: ab initio, semi-empirical, or molecular mechanics. The first and second methods are based on quantum mechanics about a model of the molecule as a number of negatively charged electrons surrounding a collection of positively charged nuclei. The third option of molecular mechanics is based on classical Newtonian mechanics about a model of the molecule as a number of mechanical bonds linking the atoms together, and these bonds can be stretched and bent according to empirical force fields. When either the Schrödinger equation or the Newtonian equation is solved with the initial spatial distribution of nuclei, in what is called the single-point determination, the binding energy of the molecule is obtained. If we make random perturbations of the positions of the various atoms, and repeat the single-point calculations, we can map the energy levels of the molecule in a neighborhood. The most stable or equilibrium position of the molecule is the one with the lowest energy in the neighborhood, and the search for this equilibrium position of the atoms is called geometry optimization. The most rigorous and accurate method of calculation is the ab initio method, which is also the most demanding in computational time and resources, so that it is most often used for smaller molecules.