Quantum theory deals with very small size scales--atomic and subatomic. Relativity deals with large scales of planets, stars and galaxies.
Relativity says that space (space-time to be precise) is curved by matter. Quantum theory has a fuzzier notion of space, currently thought of in terms of either strings or loops.
The future in relativity is, in principle, predictable, or "deterministic." Quantum physics has an unavoidable element of uncertainty. This is not dependent on instrument precision or human error, but a built-in feature of reality.
Quantum theory assigns properties of "color" and "spin" to particles. Despite the familiar-sounding words, they have no counterpart or easy explanation in everyday experience (as does electrical charge, for example).
"Frame Dragging" is an effect where a dense, rotating object warps the space around itself. University of Toronto's "Tests of General Relativity" describes the concepts and proofs of frame-dragging.