You don't need a crystal to oscillate, any reactive component, like a capacitor or inductor, with an amplifier can do the job. In fact, a crystal is equivalent to an R, L and C in series, all in parallel with a C. The advantage of a crystal is that the resonant frequency is very precise. To generate higher frequencies, people use other resonant components (e.g. inductors and capacitors inside chips) in their oscillator circuit.
With some oscillator circuits the frequency can be varied with an applied voltage (VCOs). These are used to generate high frequencies accurately, by dividing the output frequency and comparing it to an accurate low frequency source like a crystal then adjusting the control voltage appropriately. A PLL (phase locked loop) is one example, which generates a voltage proportional to the difference in phase between the divided high frequency clock and the reference clock.