Most Chinese characters have two parts, a radical and a phonetic. So different ways to simplify them might include the following:
1) Simplify the radical, retain the phonetic. Example: 调
2) Simplify the phonetic, retain the radical. Example: 这
3) Simplify one or the other of the above, for a character that has only one, but not the other. Example: 车
4) Substitute a single "character" for both parts. Example: 后
Is this roster complete? One way that I haven't seen is that both the radical and phonetic are simplified. Is this true, and if so, why might that be?