The dynamics of open quantum systems and the concept of decoherence are important aspects in understanding the appearance of noise in quantum systems as well as the connection between classical physics and quantum mechanics. New fields such as quantum information and nanotechnology require detailed analysis of the limits and possibilities set by the fact that textbook quantum mechanics with ideal and isolated systems is not adequate for describing more realistic physical systems. In these lecture notes I shall discuss the concept of decoherence in quantum systems, address the description of Markovian dynamics of open quantum systems, including simulations with quantum jumps, and then extend some of these concepts to a certain type of non-Markovian dynamics that can arise in quantum systems which are coupled to some environment possessing nontrivial spectral structure.