  We suggest a new class of hyperbolic metamaterials for THz frequencies based
on multilayer graphene structures. We calculate the dielectric permittivity
tensor of the effective nonlocal medium with a periodic stack of graphene
layers and demonstrate that tuning from elliptic to hyperbolic dispersion can
be achieved with an external gate voltage. We reveal that such graphene
structures can demonstrate a giant Purcell effect that can be used for boosting
the THz emission in semiconductor devices. Tunability of these structures can
be enhanced further with an external magnetic field which leads to the
unconventional hybridization of the TE and TM polarized waves.
