We show that quantum wells can be used as sources of controllable terahertz (THz) radiation. Excitation with an ultrafast laser pulse promotes charge carriers to the conduction band of a dc biased quantum well system. The induced wave packet oscillates back and forth through the structure and radiates in the THz frequency regime. In the devices considered, the radiation is tunable over a wide frequency range by varying the magnitude of the bias field. The amplitude of the emission can be altered by adjusting the frequency of the excitation laser. Pairs of phase-locked pulses can induce wave packets that interfere coherently with each other. The resulting THz signal is enhanced, diminished, or shifted by adjusting the delay time between excitation pulses. The THz emission can also be "sculpted" to possess desired characteristics. Two examples are considered in the text. First, we show that an optimized THz waveform can invert the population in a two-level system with a resonant pi pulse. As a second example, we demonstrate selective population of vibrational levels in a diatomic molecule. Excitation to specific levels, as well as population of a desired distribution of levels, can be achieved. Finally, we discuss future applications of these ideas and the feasibility of using quantum well structures to produce intense, far-IR bursts of radiation.