The notions of objective time and subjective time are reviewed and the relativity that obtains in case of each in different specific circumstances is discussed. Various aspects of subjective time perception have been discussed such as retrospective and prospective paradigms, frequency of neural oscillations, neural recruitment, information processing rate, centralized versus distributed timing mechanisms, State Dependent Networks (SDN), emotional states, attention, memory, psychological disorders and neuropharmacology of time perception. For objective time, its relativity in special and general theories, multidimensionality, existence of closed time-like curves, arrows of time, cyclicity of cosmic time, the time energy-time and space-time uncertainty relations have been discussed. Among the arrows of time the psychological arrow falls in the subjective category while the other arrows are on the objective side. As a possible resolution of the conflict of supremacy of one arrow over the others or of one arrow generating the others, it is argued that the psychological arrow may be the fundamental one which generates the rest of the arrows. The cross-disciplinary relevance of the article is emphasized and some important philosophical positions on the notion of time and its division into past, present and future are also discussed.