A system is a collection of components that are connected in such a way as to function as a whole .An impulsive system, on the other hand, is a general word,we use to describe systems that are subject to jumps, shocks in the state variables describing them. The shock or jumps take place very fast within short period of time when compare to evolution time of the whole system.In this monograph, we study a variety of dynamical systems of impulsive family with applications in form of models to illustrate and justify the importance of such systems to real life. We concentrate on some selected methods and models in impulsive systems. The methods/topics considered are: Strange behaviors of impulsive systems. Fixed and variable times impulsive systems. ‘Beating effect’ or ‘pulse phenomenon’ and applications to interconnecting systems and impulsive human response systems. Stability concepts in quantitative and qualitative ways and applications to autonomous and non-autonomous systems, linear and nonlinear systems.Measure differential equations, stability with respect to invariant sets and applications.Lyapunov Stability on manifolds.The methods are applied to some Models.