  We review the basic ideas of the Tensor Renormalization Group method and show
how they can be applied for lattice field theory models involving relativistic
fermions and Grassmann variables in arbitrary dimensions. We discuss recent
progress for entanglement filtering, loop optimization, bond-weighting
techniques and matrix product decompositions for Grassmann tensor networks. The
new methods are tested with two-dimensional Wilson--Majorana fermions and
multi-flavor Gross--Neveu models. We show that the methods can also be applied
to the fermionic Hubbard model in 1+1 and 2+1 dimensions.
