  We review the component Lagrangian construction of the supersymmetric higher
spin models in three dimensional (3D) Minkowski and anti de Sitter (AdS)
spaces. The approach is based on the frame-like gauge invariant formulation,
where massive higher spin fields are realized through a system of massless
ones. We develop a supersymmetric generalization of this formulation to the
Lagrangian construction of the on-shell N=1, 3D higher spin supermultiplets. In
3D Minkowski space we show that the massive supermultiplets can be constructed
from one extended massless supermultiplet by adding the mass terms to the
Lagrangian and the corresponding corrections to the supertransformations of the
fermionic fields. In 3D AdS space we construct massive supermultiplets using a
formulation of the massive fields in terms of the set of gauge invariant
objects (curvatures) in the process of their consistent supersymmetric
deformation.
