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This thesis presents the general structure of non-conformal higher-spinsupercurrent multiplets in three and four spacetime dimensions. Suchsupercurrents are in one-to-one correspondence with off-shell masslesshigher-spin gauge supermultiplets, some of which are constructed in this thesisfor the first time. In the first part of the thesis, we propose a new off-shellformulation for a massless integer superspin multiplet, whose gauge-invariantaction involves an unconstrained complex superconformal prepotential, inconjunction with two types of compensators. Next, we deduce the structure ofconsistent non-conformal higher-spin ${\cal N}=1$ supercurrents. Explicitexpressions for such supercurrents are derived for various theories in 4D${\cal N}=1$ Minkowski and AdS superspaces. These include a model of $N$massive chiral superfields with an arbitrary mass matrix, along with freetheories of tensor and complex linear superfields. The second part of thethesis is devoted to ${\cal N}=1$ and ${\cal N}=2$ supersymmetric higher-spintheories in 3D AdS space. Two dually equivalent off-shell Lagrangianformulations for the massless multiplets of arbitrary superspin in (1,1) AdSsuperspace and their corresponding supercurrents are derived. With regards to(2,0) AdS supersymmetry, we identify a multiplet of conserved higher-spincurrents in models for a chiral superfield, which is then used to construct twoseries of a massless half-integer superspin multiplet. Finally, our (2,0) AdSsupermultiplets are reduced to (1,0) AdS superspace, yielding four series of${\cal N}=1$ supersymmetric higher-spin models. Further applications of thesemassless models are discussed, one of which is related to the construction oftwo new off-shell formulations for the massive ${\cal N}=1$ gravitinosupermultiplet in AdS.

Off-shell higher-spin gauge supermultiplets and conserved supercurrents