Into the future, technically yes. Into the past, no.
For the future, you can use this method: according to Einstein's theory of relativity, time slows down when you speed up. For most situations, the effect is negligibly small, but at high speeds (as in, close to the speed of light), it is noticeable. Now, you can use this to effectively slow down time for yourself, thereby travelling into the future. For instance, suppose you got in your spaceship and went close to the speed of light, and kept that speed up until you'd spend 10 years on the ship. When you landed on Earth, you'd find that a lot longer time had passed, say 100 years. This effect has been confirmed by experiments with very precise atomic clocks, but apart from that, it's very difficult to get up to the speeds necessary to use it for anything useful.
For the past, there is currently no known method by which we can do this- as far as we know, sending information of any kind into the past seems impossible (which automatically invalidates sending anything else into the past as well). There is the occasional theoretical proposal, but usually they don't hold up to detailed analysis, and so far none has ever been validated.