We discuss the implications of the first systematic observations of solar flares at submillimeter wavelengths, defined here as observing wavelengths shorter than 3 mm (frequencies higher than 0.1 THz). The events observed thus far show that this wave band requires a new understanding of high-energy processes in solar flares. Several events, including observations from two different observatories, show during the impulsive phase of the flare a spectral component with a positive (increasing) slope at the highest observable frequencies (up to 405 GHz). To emphasize the increasing spectra and the possibility that these events could be even more prominent in the THz range, we term this spectral feature a "THz component". Here we review the data and methods, and critically assess the observational evidence for such distinct component(s). This evidence is convincing. We also review the several proposed explanations for these feature(s), which have been reported in three distinct flare phases. These data contain important clues to flare development and particle acceleration as a whole, but many of the theoretical issues remain open. We generally have lacked systematic observations in the millimeter-wave to far-infrared range that are needed to complete our picture of these events, and encourage observations with new facilities.