Memory function formalism or projection operator technique is an extremely useful method to study the transport and optical properties of various condensed matter systems. A recent revival of its uses in various correlated electronic systems is being observed. It is being used and discussed in various contexts, ranging from non-equilibrium dynamics to the optical properties of various strongly correlated systems such as high temperature superconductors. However, a detailed discussion on this

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... hod, starting from its origin to its present day applications at one place is lacking. In this article we attempt a comprehensive review of the memory function approach focusing on its uses in studying the dynamics and the transport properties of correlated electronic systems.