Binary Mixtures (Binary Alloys or Binary Fluids) exhibit phase separation after a sudden quench below the critical temperature. Domain growth occurs due to the motion of interfaces between deferent phases. The dynamical aspects of phase separation and the domain growth laws have been studied and explored by the physicists in great deal from several decades. There exist various theoretical, experimental or computational methods to dig into the underlying physics. We focus to shed light on this phenomenon and review the framework of mean field theoretical study, phase-field modelling and simulation techniques. We further discuss about the recent advancements in this field particularly on the use of Cahn-Hilliard equation with activity parameter to describe the active phase separation dynamics.