I review the AdS/CFT (anti-de Sitter/conformal field theory) dualities within the framework of the general theory of unitary lowest-weight (ULWR) (positive-energy) representations of non-compact spacetime groups and supergroups. The ULWRs have the remarkable property that they can be constructed by tensoring some fundamental ULWRs (singletons or doubletons). The conformally invariant theory in d dimensions to which M/superstring theory over AdS_{(d + 1)}×S^p is dual to is a singleton or doubleton field theory. One can work either in a manifestly unitary compact `particle' basis (Wigner picture) or manifestly covariant non-compact `coherent state' basis (Dirac picture) of the ULWRs of conformal (super)groups. These coherent states are labelled by spacetime coordinates and correspond to covariant fields with definite conformal dimensions. On the other hand, the supercoherent states of the ULWRs of superconformal algebras correspond to superfields. These results extend to higher-dimensional generalized spacetimes (superspaces) defined by Jordan (super)algebras and Jordan (super)triple systems. In particular, they extend to the ULWRs of the M-theory symmetry superalgebra OSp(1/32,R).