We present theoretical results on the nonlinear optics of semiconductor quantum wells in intense THz electric fields (the dynamic Franz-Keldysh effect or DFKE). The absorption spectra show a rich variety of behavior, including THz replicas of the 2p exciton and THz sidebands of the 1s exciton. We calculate the dependence of these features on the phase and intensity of the THz field using the extended semiconductor Bloch equations, and discuss the relevance of our results to future experiments. The 1s-sideband absorption feature shows a strong dependence on the phase of the THz field, and phase averages to zero. We also discuss the relative advantages and disadvantages of reflectivity and absorption spectroscopies for probing the DFKE.