  The N = 1 superfield formalism in four-dimensions is well formulated and
understood, yet there remain unsolved problems. In this thesis, superfield
actions for free massless and massive higher spin superfield theories are
formulated in four dimensions. The discussion of massless models is restricted
to half integer superhelicity. These models describe multiplets with helicities
(s, s-1/2) where s is an integer. The investigation of massive models covers
recent work on superspin-3/2 and superspin-1 multiplets. Superspin-3/2
multiplets contain component fields with spins (2, 3/2, 3/2, 1) and superspin-1
multiplets contain component fields with spins (3/2, 1, 1, 1/2). The super
projector method is used to distinguish supersymmetric subspaces. Here, this
method is used to write general superspace actions. The underlying geometrical
structure of superspace actions is elucidated when they are written in terms of
super projectors. This thesis also discusses the connection between
four-dimensional massive theories and five-dimensional massless theories. This
connection is understood in non-supersymmetric field theory but has not been
established in superspace. A future direction of the five-dimensional models
would involve finding an anti-de Sitter supergravity background. In order to
construct this model using the knowledge gained from this thesis, an
understanding of the Casimir operators of four-dimensional anti-de Sitter
superspace would be necessary. These Casimir operators have not yet appeared in
the literature and are presented in this thesis.
