In this talk, we discuss the dynamics of a general non-autonomous dynamical system. In particular, we discuss notions like equicontinuity, minimality and various notions of mixing and sensitivities for a general discrete non-autonomous system. We also discuss the case when the dynamics is generated by a uniformly convergent sequence of maps. We prove that if the system is generated by a commutative family converging at a “sufficiently fast rate” then many dynamical notions for non-autonomous system can be characterized by the limiting (autonomous) system.