The pickups used by many manufacturers are transducers, devices which convert energy. Electric ukuleles are usually provided with piezoelectric pickups, which feature embedded crystals that create energy when mechanically agitated, i.e. when the strings vibrate.
There are active and passive piezo pickups, and also newer systems like Nanoflex. Premium manufacturers like to use passive pickups, as they are barely noticeable on the outside. They are also not overly sensitive, affordable, and don't require batteries.
The preamp featured in active systems is often provided with various "extras". For example, most preamps feature an active equalizer (EQ) which is an effects device which affects the frequency response and is mainly used to control the sound. Rib preamps often feature an integrated tuner.
Another popular feature is the so-called notch filter. This is a special EQ which you can use to implement an extremely thin and deep cut into a predefined frequency band. This helps partially or fully eliminate interfering frequencies (e.g. bass feedback, mains hum).
Ukuleles without pre-installed pickups can be retrofitted or recorded using mics.
B-Band U1.3T Ukulele Pickup Set
Fishman PRO-AG0-UKE Ukulele Pickup