This may result in causing quiet sounds that occur between loud sounds to be turned down as well. There's also a danger with setting release times too fast. Quick release times will make the compression effect too noticeable, to the point where you can hear a very unnatural 'pumping' or 'breathing' sound as the signal level goes up and down. In general, the release should be set fast enough to recover in time to process the next bass slap, power chord or drum hit. Again, like the attack control, some budget compressors might not include a release time control.
Some models simply have switches for 'slower' and 'faster' release.
If there is no release control at all, the manufacture has designed the compressor to use a release time to fit the most common musical situations. Some compressors have an additional control called a peak level control and like the threshold control, it's expressed in dBs. Using this control, you can set a level which will not be exceeded at the output, even when you have a very quick, loud sound, such as a snare drum hit. Additionally, you'll probably have an output gain control to set the final output level. This is needed because the compressor is reducing the level of signals that cross the threshold, so an additional stage of gain is used to bring the signal back up to a nominal level.