We study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self-maps on a compact space X. We derive necessary and suﬃcient conditions for the system to exhibit complex dynamical behavior. In the process we discuss properties like transitivity, weakly mixing, topologically mixing, minimality, sensitivity, topological entropy, and Li-Yorke chaoticity for the non-autonomous system. We also give examples to prove that the dynamical behavior of the nonautonomous system in general cannot be characterized in terms of the dynamical behavior of its generating functions. © 2017 Topology Proceedings.