Dual-band or multi-band compression:
The basic idea is that your instrument signal gets split into two or more frequency ranges using a crossover. So for example it gets divided into lows and highs, with little overlap between them. Then each "band" runs through separate, independent compressor circuits. Then the compressed signals get recombined back into one mono signal of full frequency range. The benefit is that strong signal peaks in one range, passing the threshold and triggering the compression, will not cause the other frequency range to also be compressed. It is common with regular single-band compressors for the highs to be "swallowed" (attenuated too much) when a low note triggers the compression, as the compressor will reduce the signal levels of everything at that moment.
So if you play quickly up and down the fretboard or keyboard, or if you mix strong aggressive playing on a low string with more nuanced playing on the higher strings, then a multi-band compressor will allow greater articulation, clearer tone, and more even signal levels across the full range of the instrument. However there are "cons" as well: there may be audible artifacts if the crossover component is not well-designed. The lows of a bass will often seem cut back, less deep or powerful, due to the greater relative presence of the highs and mids. And some compressor users just prefer the sonic effect of the traditional single-band comps.
In general I recommend multi-band compression for tappers, slappers who want a bright sound, people who play a lot of harmonics and ghost notes, extended-range instrumentalists, and others who find compression takes too much away from the detail of their sound while playing across a wide frequency range. For most other players -especially ones who prefer smooth squish, deep boom, or a more "glued together" sound quality- I recommend traditional single-band compression.
Here are the dual/multi-band comps I can think of at the moment:
Trace Elliot SMX
FEA Dual Band
Digitech Bass Squeeze
TC Electronic C300, Nova Dynamics, and Triple C
Ashdown Bass Comp
Aphex Dominator 720
Many other rack comps have a feature that allows you to leave the low frequencies uncompressed, via a sidechain, and this can offer results somewhat like dual-band compression... as long as you wanted less compressed lows. A common example is the dbx 166A/XL "Contour" button. The Focusrite Compounder has a similar feature with its "Huge" button, mixing uncompressed lows in with the compressed full-range signal. Again, several other manufacturers make units with this type of function--you just have to figure out the "hidden meaning" of whatever cryptic name they gave that button or knob.