According to Wikipedia, fantasy is comprised of two main sub-genres: high fantasy, and the so-called "sword and sorcery" fantasy (whatever that is...). These two, while fairly encompassing, seem to leave many loopholes and bad combinations. Here's how I see it:
|Highest of fantasy|
What, then, is modern fantasy? Here are any books that create a fantastic world alongside the real world. These are books that use our world and add to it magical or fantastic elements. Harry Potter, then, for all its adventurous and romantic roots, would fall squarely into the modern category. The brunt of creature based fantasy, or urban fantasy (Twilight, etc.) would also be called modern.
So is fantasy only defined by these two? Obviously not. No genre is ever fully encompassed by two generalizations. But these two subjects cover a lot of ground, enough to satisfy me. You'll have to tell me if you agree or disagree.