A timely topic, if you'll pardon the pun. It's very much a live issue in contemporary philosophy and as you'd guess, there is more than one camp.
Very roughly, we can carve the territory up this way:
Presentists say that only the present is real. The future does not exist, and will only come into being after the present has slipped away. One reason why some people defend presentism is that they believe it does more justice to our sense of the passage of time. On this view, things "become."
Eternalists think that all events are equally real. There is no special moment that counts as "the present." Rather, for any given moment, there are earlier and later moments. One reason (though not the only one) why some people defend eternalism is that it seems to fit better with the understanding of space and time that we get from the theory of relativity. Think of it this way. Suppose an event happens outside my window as I'm writing this—say, a car backfires. And suppose that on a planet far away in another galaxy, there's a certain event—an explosion, say—that happens, but as it works out no light signal, no matter how powerful, could get from here to that explosion, not could any other signal. To put it in the language of relativity, suppose the explosion on the other planet is outside the lightcone of the the backfire of the car. In that case, relativity says there's simply no answer to the question of which event happened first: backfire or explosion. In fact, if we say that only the present is real, we have no good way of saying what's part of the supposed present of any event.
That's a bit quick and dirty, but it may help give you the bigger picture. There's a big literature on this topic. One reader-friendly place to start is with Craig Callender's little book Introducing Time . Don't be put off by the fact that it has lots of cartoon pictures. It's very good. And you can even download it as an ebook.