  This thesis is dedicated to the study of (super)spin projection operators and
their applications on maximally symmetric (super)space backgrounds in three and
four dimensions. On such backgrounds, the irreducible representations of the
associated isometry (super)algebra may be realised on the space of tensor
(super)fields satisfying certain differential constraints. The (super)spin
projectors isolate the component of an unconstrained (super)field which
furnishes the irreducible representation with maximal (super)spin. The explicit
form of these (super)projectors are found in the following backgrounds:
three-dimensional ($3d$) $\mathcal{N}$-extended Minkowski superspace
$\mathbb{M}^{3|2 \mathcal{N}}$; $3d$ (anti-)de Sitter space (A)dS$_3$; $3d$
$\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{3|2}$; four-dimensional
($4d$) $\mathcal{N} = 1$ anti-de Sitter superspace AdS$^{4|4}$; and $4d$
$\mathcal{N} = 2$ anti-de Sitter superspace AdS$^{4|8}$. An array of novel
applications are investigated, with an emphasis placed on the interplay between
(super)projectors and (super)conformal higher-spin theory. Another major
component of this thesis consists of a detailed study of massless higher-spin
gauge models with $\mathcal{N} = 2$ AdS supersymmetry in three dimensions. We
find that every known higher-spin theory with $(1, 1)$ AdS supersymmetry
decomposes into a sum of two off-shell $(1, 0)$ supermultiplets which belong to
three series of inequivalent higher-spin gauge models.
