T-symmetryT-symmetry is the symmetry of physical laws under a time reversal transformation (replacing 't' by '-t' in all the equations). All laws of classical physics exhibit this nice T-symmetry. To say simply, all classical phenomena are reversible in time (Here 'classical', includes relativistic descriptions as well and only excludes quantum phenomena). By common sense, you might think that T-symmetry is obviously violated: we cannot remember the future, eggs are much easier to break than to reconstruct; in general, entropy increases. This is called the second law of thermodynamics, but in fact is not related in any obvious way to T-symmetry. The second law can be entirely attributed to the "initial conditions" of the universe, rather than the laws governing evolution.
Many physicists believe T-symmetry is violated. This is because experiments have shown that CPT-symmetry holds, but that CP-symmetry is broken. It can be shown that if CP-symmetry is broken, there must be a balancing T-symmetry violation in order to preserve CPT-symmetry.
However, there is no consensus as to the exact nature of the T-symmetry violation. Gravity is a prime contender: the fact that gravity is only attractive, not repulsive, may point to a violation of T-symmetry. Black holes appear to violate T-symmetry: there are significant differences between black hole formation and evaporation (via Hawking radiation). Particle physicists are conducting experiments looking for T-symmetry violation in high-energy nuclear reactions.