Through the observational study of stellar pulsations, the internal structure of stars can be probed and theoretical models can be tested. The main sequence γ Doradus (Dor) and δ Scuti (Sct) stars with masses 1.2-2.5 M&sun; are particularly interesting for asteroseismic study. The γ Dor stars pulsate in high-order gravity (g) modes, with pulsational periods of order of one day. The δ Sct stars, on the other hand, show low-order g and pressure (p) modes with periods of order of 2 hours. Theory predicts the existence of `hybrid' stars, i.e. stars pulsating in both types of modes, in an overlap region between the instability strips of γ Dor and δ Sct stars in the Hertzsprung-Russell diagram. Hybrid stars are particularly interesting as the two types of modes probe different regions of the stellar interior and hence provide complementary model constraints. Before the advent of Kepler, only a few hybrid stars had been confirmed. The {{Kepler}} satellite is providing a true revolution in the study of and search for hybrid stars. Analysis of the first 50 days of {{Kepler}} data of hundreds of γ Dor and δ Sct candidates reveals extremely rich frequency spectra, with most stars showing frequencies in both the δ Sct and γ Dor frequency range. As these results show that there are practically no pure δ Sct or γ Dor pulsators, a new observational classification scheme is proposed by cite{Grig10}. We present their results and characterize 234 stars in terms of δ Sct, γ Dor, δ Sct/γ Dor or γ Dor/δ Sct hybrids.