Necessary and sufficient conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are given in terms of asymptotic stability. The relation between generalized synchronization, predictability, and equivalence of dynamical systems is discussed. All theoretical results are illustrated by analytical and numerical examples. In particular, the existence of generalized synchronization in the case of parameter mismatch between coupled systems leads to a new interpretation of recent experimental results. Furthermore, the possible application of generalized synchronization for attractor reconstruction in nonlinear time series analysis is discussed.