Short-period planets are a gift from nature that allowed the rapidacceleration of exoplanetary science. They are more readily studied than long-period planets, and their existence and orbital properties pose interesting questions. I will present the results of a search for the shortest-period transiting planets, using data from the Kepler spacecraft. The results show that 0.5% of Sun-like stars have orbiting "lava worlds": terrestrial planets with periods ranging from 4 hours to one day. The search also revealed a new class of objects that seem to be small rocky planets disintegrating in the blazing heat from their parent stars. Finally, I will describe an upcoming NASA mission, the Transiting Exoplanet Survey Satellite (TESS), which will identify thousands of short-period planets around the nearest and brightest stars in the sky.