One of the two most basic filter circuit types. A basic RC filter consists of only two components: a resistor and a capacitor. An RC filter can be made to work on any type of circuit; it has essentially infinite headroom and it is a completely passive circuit (requires no power). Depending on how the components are connected in the circuit, the RC filter can act as either a high pass or a low pass filter. It is a single-pole filter with a slope of 6 dB/octave, although multiple stages can easily be combined to build multi-pole filters with steeper slopes.
The cutoff frequency of a RC filter is determined by the formula F = 1/2πRC, where R is the resistor's value on ohms, and C is the capacitor's value in farads. To make the cutoff frequency variable, the usual practice is for some of the resistance to be in the form of a potentiometer. RC circuits can be made to work well at audio frequencies with reasonable-sized components; there are many online tools to aid the designer in choosing good R and C values for a given frequency range.
RC filters got some use in synths, although they are not voltage controllable as such, and so the cutoff frequency can only be adjusted manually. This somewhat limits their use, although they are seen in specialized applications such as formant filters. However, the basic RC idea does serve as the basis for many VCF designs, which essentially replace the resistor with something that has an input resistance that can be electrically varied, such as the transistor in a transistor ladder filter, or the operational transconductance amplifier in an OTA filter.