what are modern openings?

I have two questions here.

1. Why are certain openings considered mondern?

2. What are some modern openings?

It would be nice if you could link the openings, since I might not know what you're talking about. Thanks!

I assume you mean 'hypermodern'?  A good starting point to understand the hypermodern movement in chess is Wikipedia: http://en.wikipedia.org/wiki/Hypermodernism_(chess).  To lift from Wikipedia, "Hypermodernism is a school of chess thought which advocates controlling the centre of the board with distant pieces rather than with pawns, thus inviting the opponent to occupy the centre with pawns which can then become objects of attack."

Examples of hypermodern openings are the Nimzo-Larsen Attack (1. Nf3 2. b3 3. Bb2 or some variation on it), many Indian defenses to d4, and to a lesser extent, openings such as the English opening and Sicilian Dragon.

Classic chess is building a large center by occupying it with pawns and trying to maintain it at all costs. This is the old school openings like the Evans Gambit where you go for a quick attack right from the onset.

The Hypermoderns preach that this type of center could be undermined by attacking it with pieces and pawns. It's more about counterattack. It includes Reti and Catalan with White, and King’s Indian, the Queen’s Indian, the Nimzo Indian, and the Grunfeld with Black.

I've always felt that it is quite possible to include a category between Classical (where the full pawn centre is the only goal) and hypermodernism (a full pawn centre is useless) which could be called modern. For example the sicilian cannot creat a full pawn centre but does attempt to prevent white from getting one.

I suppose following the definitions here Alekhines Defense would be a good example of Hypermodern too?

Yes, it would, as black lets white build up a large pawn center and then tries to undermine it.  The Wikipedia article I mentioned lists it as an example of a hypermodern defense.