Filter design is one of the most interesting aspects of electrical engineering. This is in no small part due to the wide variety of topologies and configurations available for each kind of filter. In the early days, filters were passive — made exclusively of resistors, caps and inductors — but since the advent of low-cost, low-distortion op-amps, active filters have become much more prominent. One of the greatest benefits of active filters is that they don’t require inductors, so size and weight are kept to a minimum.
App note 1762 from Maxim is a good survey of common active filter topos, and explains the strengths and weaknesses of each one. The basic topologies can be extended with more advanced techniques, such as voltage control or switched capacitors, but the underlying configurations are the same.