Sawteeth oscillations are periodic relaxations of the core plasma density and temperature in tokamaks. The rise of the temperature due to external heating is terminated by the crash phase, which involves magnetic reconnection. This is the case of fast magnetic reconnection in collisionless plasmas (Lundquist number S≥108) with a strong guide field. (The toroidal magnetic field in a tokamak is a few orders larger compared to the reconnected helical field.) Experimental measurements show non-linear behavior before and during the crash phase. Simplified single-fluid models are not able to explain the reconnection dynamics during the crash, and two-fluid effects have to be considered. In this case, numerical simulations give good agreement with the observations for the crash duration. At the same time, the present simulations explain experimentally observed phenomena only partially, and several questions remain an area of active research: evolution during the crash, the onset of the fast phase, the existence of the post-cursors, the degree of stochasticity, and others. This overview paper summarizes the current understanding of the crash process, highlights remaining problems, and shows connections to magnetic reconnection research in other plasmas.