We study string propagation on AdSs times a compact space from an "old fashioned" worldsheet point of view of perturbative string theory. We derive the spacetime CFT and its Virasoro and current algebras, thus establishing the conjectured AdS/CFT correspondence for this case in the full string theory. Our results have implications for the extreme IR limit of the Dl -D5 system, as well as to 2+1 dimensional BTZ black holes and their Bekenstein-Hawking entropy.

We review some aspects of the interplay between the dynamics of branes in string theory and the classical and quantum physics of gauge theories with different numbers of supersymmetries in various dimensions.

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We argue that vacua of string theory which asymptote at weak coupling to linear dilaton backgrounds are holographic. The full string theory in such vacua is "dual" to a theory without gravity in fewer dimensions. The dual theory is generically not a local quantum field theory. Excitations of the string vacuum, which can be studied in the weak coupling region using worldsheet methods, give rise to observables in the dual theory. An interesting example is string theory in the near-horizon background of parallel NS5-branes, the CHS model, which is dual to the decoupled NS5-brane theory ("little string theory"). This duality can be used to study some of the observables in this theory and some of their correlation functions. Another interesting example is the "old" matrix model, which gives a holographic description of two dimensional string theory. 8/98