To understand quantum dynamics it is essential to realize that observable systems are always subsystems of a larger one — ultimately of the whole universe. The notion of an isolated system makes sense only as an approximation depending on the concrete situation. This point of view has been emphasized in the preceding chapters as the basis of the whole book. This chapter presents a self-contained discussion of the exact dynamics of a subsystem and of the Markovian approximation including the stochastic Schrodinger equations. These equations are then formally identical with stochastic modifications of the Schrodinger equation which have been proposed by some authors as a priori modifications of the Hamiltonian dynamics and which will be discussed in Chap. 8.