We present a theoretical description of time-resolved photoemission in charge-density-wave insulators that derive their ordering from electron nesting effects. In these pump/probe experiments, a large amplitude (but short duration) pump pulse excites the system into nonequilibrium and then a higher frequency low amplitude probe pulse photoexcites electrons, which are measured at the detector. We describe effects of electron correlations on the photoelectron spectroscopy and provide details for the theoretical techniques used to solve these problems. We also show how the gap fills in as the system is excited, even though the order parameter does not go to zero. The theory is developed for the Falicov-Kimball model, which can be solved exactly with nonequilibrium dynamical mean-field theory.