The paper confronts two perspectives on the asymmetry of time: a philosophical and a physical one. From the philosophical perspective, time has fundamental asymmetries which together form an asymmetry of time: there seems to exist something like a distinguished Now moving toward the future; we have many traces of the past - both in our memory and in the external world - but no traces of the future; events from the past influence those from the future, but we have no evidence of backward causation; the future seems to be open and we definitely cannot change the past. Because we believe in physics as a fundamental theory describing the world, we expect that physics should explain all of these asymmetries. However, the rub lies in the fact that physics, as it is known at present, is unable to explain these asymmetries. This means that physical processes such as the entropy increase, the expansion of the Universe or those in which weak interactions are involved only form asymmetries in time, that is, they just represent some asymmetrical physical processes in time. The way out of this difficulty can be sought in two directions: either we can look for a fundamental temporally irreversible law of nature which would be able to explain the temporal asymmetries of the world or we should look for the solution of the issue at hand outside of physics, that is, in metaphysics. The paper shows the difficulties of both directions of research.