The main differences between compact cameras and DSLRs are mainly 3:

1. Sensor size: compact cameras have small sensors, that give you little space to play with shallow depth of field, and give you a smaller dynamic (the ability to catch in the same shot bright and dark objects keeping details in both).
2. Ability to use multiple, different, lenses: above a critical threshold, good lenses are more important than sensors. On compact cameras you can't change lens.
3. Manual controls, ergonomics and speed: DSLRs let you control everything in a shot if you want, and are designed to let you do these changes fast, so you can take a shot in less time.

Usually high end "compact" cameras are called "bridge cameras", and while still having small sensors and fixed optics, they may have also manual controls, but they aren't as comfortable as those in DSLR.

Recently the place between these cameras and dslrs has been taken by a new category, of so called mirrorless cameras. Usually they have replaceable lenses and bigger sensors (some of them, like the Canon EOS-M, have exactly the same sensor of a dslr), so they may give you images similar to the ones taken with DSLRs, but still being a lot smaller than usual DSLRs. Still, their ergonomics will be more like a compact camera than a DSLR, that could be a good or bad thing, it depends on your tastes.

Anyway, if you can afford them, mirrorless are a lot smaller and more portable cameras than dslr, still giving you control and some of the advantages of DSLRs.