Split-band processing is one of the easiest ways to compress transparently. Broadcast stations use split-band compression regularly, often dividing the spectrum into four or five bands. When it's done right, the radio station sounds great: loud, present, with no squashing or pumping.
The great Dolby noise reduction systems, from Dolby A all the way through B, C, S and SR, all use some variation on compression, expansion and band-splitting.
Split-band techniques work well for several reasons: You can optimize each set of dynamics processors (the compressor, expander and limiter) to a particular range of audio frequencies. That is, the ratio and threshold controls can be suited to each part of the spectrum.
You can decide to process different ranges of an instrument differently. You could use no compression on the low end of a bass, with heavy compression on the top end to put the string slaps in balance with the bottom. Or you could tighten a boomy bottom with compression but leave the top less controlled for an open feeling.
Any massive anomaly like a low frequency breath noise for example, only triggers gain reduction within its range, leaving the desired vocal unaltered. And the decidedly unmusical phenomenon of a popped "p" sucking the overall level back 10 dB is eliminated.

The following tips refer to a compressor design featuring one input with two internal signal paths, each with its own compressor and fed from an adjustable crossover, then summed back together and exiting as one output, as shown here.
A lower stage volume is beneficial in getting a better house mix. Split-processing techniques can achieve a lower volume without sounding tinny.
On-stage big 4 x 12" cabinets create a huge wall of sound, but are often accompanied by an annoying woofing on the low-end. Try setting a crossover point around 400 Hz and compress the bottom-end at a 10:1 ratio. Play a chord where you notice a lot of woofing then set the gain reduction with the threshold control to read 6 dB on the display. If you hit an open chord and there is no gain reduction then it is set right. Compress the top end using a 1.5:1 to 2:1 ratio, along with a 3 dB gain reduction when an open chord is hit. This gives your sound more attack. Play around with these settings. When correct for your instrument, no matter where you play on the neck the bottom-end will sound even, without woofing, giving your overall tone punch and clarity.
Be careful not to over compress the top-end, or the pick attack will slur. If you want more attack, turn up the top-end level.
Solve the problem of overdriving the system by using a split-band compressor to keep the high-end attack, without low-end booming. For more attack, turn up the level on just the high-end.
Begin with a crossover setting of 200 Hz and set the low-end band for mild compression, around 2:1, with the threshold set at -10 dBu. Try setting the high-end band for heavy compression at 6:1, and the threshold at -20 dBu. Turn the volume and the treble controls on the bass full up, and slap and pop hard. You should hear that the high-end is pushed down to the low-end level, yet sounds balanced and not compressed.
Each instrument is different so experiment until pleased with the result. Sometimes slight processing on the lows will tightened the bottom end without sounding controlled or processed. The highs with subtle compression will sound natural without a breathing sound.
Use split-band compression on bass guitar, piano, drums, vocals, anywhere you normally use a compressor. It gives you more control with a less tortured sound. It even sounds good compressing an entire mix.
Of special interest are instruments with large level changes in their different tonal ranges. String pops on a bass are one, but flute is another. The higher tones require more breath and are much louder than the lower.
The split-band approach allows you to apply different amounts of compression to the low- and high-ends of a piano, or you can limit just the high end of the sax.
A split-band compressor does a better job of smoothing the performance out.