  We review the recently developed general gauge invariant approach to
Lagrangian construction for massive higher spin fields in Minkowski and AdS
spaces of arbitrary dimension. Higher spin Lagrangian, describing the dynamics
of the fields with any spin, is formulated with help of BRST-BFV operator in
auxiliary Fock space. No off-shell constraints on the fields and gauge
parameters are imposed. The construction is also applied to tensor higher spin
fields with index symmetry corresponding to a multirow Young tableau.
