We published a high fantasy story from Peak before. Check it out here while you're waiting for the new issue.
Of course, the subdivisions of fantasy literature are many. Closely related to high fantasy is epic fantasy. Epic fantasy is fantasy that is defined by the epic nature of the characters, plot, and/or themes. Notice most epic fantasy is also high fantasy. Famous examples here include the classics The Lord of the Rings, The Chronicles of Narnia, A Song of Ice and Fire.
Interestingly, we don't get a lot of high or epic fantasy stories. Think about submitting one, if you've got one or an idea for one.
Probably the most popular kind of fantasy these days is urban fantasy. I said the other day that urban fantasy is a fantasy set on contemporary planet Earth. Notice it definitely does not have to be set in an urban area--this is a common misconception. Urban fantasy takes place on our world; it just has fantasy element(s) added to it. Next week I'll discuss a couple urban fantasies we'll be publishing in the next issue.
Check back then! :)