A type of voltage controlled filter circuit, developed by Bob Moog in the mid-1960s. The transistor ladder uses two transistors and one capacitor per pole. The name comes from the way the circuit is often drawn in schematics, in a vertical presentation with the capacitors as the "rungs" of the ladder, and the transistors as the legs.
The circuit creates a certain amount of characteristic distortion, giving it a recognizable sound. That sound is often associated with Moog synths since it was used in most of the early Moog models, and also in the current Voyager and its derivatives. The characteristic sound becomes especially prominent when resonance is increased, and when the input signal is hot enough to drive the circuit into distortion. The circuit has many desirable properties from a design standpoint: it is easy to analyze, fairly simple to calibrate and diagnose, and inexpensive to build. Performers also appreciate the fact that it can be driven to self-oscillation at a sufficiently high resonance setting, and will produce a fairly pure sine wave when doing so. Its one complication is that the control voltage "rides through" the circuit along with the signal being filtered, so circuitry has to be added to the output to prevent control voltage feedthrough.
In the early '70s the Moog VCF sound was considered so desirable that other companies tried to develop circuits that would behave the same way but get around Moog's patent. At one point both ARP and Roland rather blatantly copied the Moog circuit and Moog had to threaten legal action to get them to desist. Among other things, this resulted in the variation known as the diode ladder, as pioneered by EMS. The Moog patent expired in 1986 and the circuit is now widely copied.