Why can't time run backwards?

We can all tell when a movie of some everyday event, such as a kettle boiling or a glass shattering, is run backwards. Similarly, we all feel that we can remember the past and affect the future, not vice versa. So there is a very clear "arrow" (direction) of time built into our interpretation of our everyday experience.Yet the fundamental microscopic laws of physics, be they classical or quantum-mechanical, look exactly the same if the direction of time is reversed. So what is the origin of the "arrow" of time? This is one of the deepest questions in physics. I will review some relevant considerations, but do not pretend to give a complete answer.