There are two main threads associated with the theoretical chemistry of the excited state. On the one hand, we have to understand the shapes of potential energy surfaces that are associated with the nonadiabatic event that occurs when the reaction path passes from one state to another. This is associated with a conical intersection. The other thread is associated with methods for computing such potential energy surfaces and possibly studying the dynamics associated with nuclear motion. The shapes of these potential surfaces result from the fact that the force field of an excited state, i.e. the strength and position of the various bonds, is different from that of the ground state. In this chapter we briefly introduce the subject of valence bond theory and how it controls the shapes of potential energy surfaces. Electronic structure methods and dynamics methods for the study of nuclear motion are huge fields. Our objective is to elucidate the general conceptual principles that lie behind these methods so the reader can make informed decisions about which methods may be most appropriate for the problem to hand. In this chapter we introduce the partitioned eigenvalue problem and the perturbation theory that stems from this partitioning.