Long GRBs are the most powerful explosions in the universe since the Big Bang. At least, some fraction of long GRBs are born from the death of massive stars. Likewise, only some fraction of massive stars that satisfy additional special conditions explode as long GRBs associated with supernovae/hypernovae. In this paper, we discuss the explosion mechanism of long GRBs associated with hypernovae: 'the central engine of long GRBs'. The central engine of long GRBs is very different from that of core-collapse supernovae, although the mechanism of the engine is still not firmly established. In this paper, we review theoretical studies of the central engine of long GRBs. First, we discuss possible progenitor stars. Then several promising mechanisms of the central engine-such as black hole and magnetar formation-will be reviewed. We will also mention some more exotic models. Finally, we describe prospects for future studies of the central engine of long GRBs.