The purpose of this thesis is to examine the temporal evolution of open quantum systems, and to give the reader an introduction to this field. We will discuss why this can not be treated in the same manor as the evolution of closed systems, and I will provide an overview of some of the alternatives. In particular it will be emphasized that some of these have a non-Markovian character while others are Markovian. We will discuss the conditions under which these descriptions may be applied, and they will be illustrated using two very simple models of open systems: an open two-level system and an open harmonic oscillator. These models will also be used to illustrate particular characteristics that open systems have relative to closed ones, such as decay, damping, heating and decoherence.