Electronic oscillators are often designed around an LC tank circuit, a tuned circuit formed with an inductor and a capacitor. But use of an inductor is not a requirement. Instead, the tuned circuit can be built using just resistors and capacitors. Such an oscillator is referred to as an RC oscillator.
Sine wave oscillators
Two configurations are common. One is called a Wien bridge oscillator (also called a "Wein Bridge"; there appears to be some disagreement about the correct spelling). In this circuit, two RC circuits are used, one with the RC components in series and one with the RC components in parallel. The Wien Bridge is often used in audio signal generators because it can be easily tuned using a two-section variable capacitor. The architypical HP 200 audio oscillator is a Wien Bridge oscillator.
The second common design is called a "Twin-T" oscillator as it uses two "T" RC circuits operated in parallel. One circuit is an R-C-R "T" which acts as a low-pass filter. The second circuit is a C-R-C "T" which operates as a high-pass filter. Together, these circuits form a bridge which is tuned at the desired frequency of oscillation.
If they are to produce an undistorted sine wave, RC oscillators usually require some form of amplitude control. Many common designs simply use an incandescent lamp in the feedback circuit. These oscillators take advantage of the fact that the resistance of the tungsten filament increases in proportion to its temperature. Operated well below the point at which the filament actually illuminates, increased amplitude of the feedback signal causes increased current flow in the filament thereby increasing the resistance of the filament. The increased resistance of the filament reduces the feedback signal, limiting the oscillator's signal to the linear range. (That is, clipping is prevented.) The HP 200 oscillator introduced this technique.
More-sophisticated oscillators measure the output level and use this as feedback to control the gain of the voltage-controlled amplifier within the oscillator. If the amplitude detector has a flat frequency response, then this negative feedback of the amplitude measurement will ensure that the oscillator has a constant output amplitude no matter what frequency it is set to generate.
Non-sine wave oscillators
Many designs exist for RC oscillators that are not required to produce a sine wave. Multivibrators are one approach. The 555 timer IC is another very common approach. Most non-sine wave RC oscillators require only a single RC network.