an active filter
An active filter adds an op-amp to the resistors and capacitors of a filter. That one active part changes everything: it can buffer the filter so the load no longer disturbs it, provide gain so the signal comes out bigger, and, cleverly used, sharpen the response far beyond what plain RC parts can do, all without a single inductor.
The key idea is that the op-amp isolates the stages. Its near-infinite input resistance means it does not load the RC network feeding it, and its near-zero output resistance means it drives the next stage without sagging, so the loading problem that plagues passive filters disappears. Better still, by feeding part of the output back into the RC network, an op-amp can synthesize the high-Q, resonant behavior that passive designs need an inductor for. A second-order section like a Sallen-Key or multiple-feedback filter does this with just an op-amp, two resistors, and two capacitors, and you cascade such sections to build any order you like.
Active filters dominate from DC up through the audio band and into the low hundreds of kHz: anti-alias and reconstruction filters, audio tone and crossover networks, instrumentation signal conditioning. The honest caveats are that an active filter needs a power supply and inherits the op-amp's limits, it cannot work on signals beyond the op-amp's bandwidth or slew rate, adds the op-amp's noise and offset, and at radio frequencies passive LC still wins. Within its range, though, the active filter is the everyday workhorse.
The simplest active filter is an RC low-pass followed by a voltage follower (unity-gain buffer). The RC sets the cutoff; the op-amp buffer presents a near-infinite input to the RC (so no loading) and a near-zero output to the world, so whatever you connect downstream no longer pulls the cutoff around.
Adding a buffer makes the filter's response immune to the load, the core advantage of going active.
An active filter is only as good as its op-amp: it cannot filter signals beyond the op-amp's bandwidth or slew rate, it adds noise and offset, and it needs a supply. For RF, passive LC still rules.