On 5D AdS SUSY and Harmonic Superspace

In our recent paper arXiv:0704.1185 [hep-th], we presented the differential geometry of five-dimensional N=1 anti-de Sitter superspace AdS^{5|8}=SU(2,2|1)/SO(4,1) x U(1) and developed the harmonic and the projective superspace settings to formulate off-shell supersymmetric theories in AdS^{5|8}. Here we give a brief review of the geometry and the harmonic superspace construction, and also elaborate on vector supermultiplets.