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What is the most comprehensive and up-to-date review of Higher Spin Theory (in particular, in AdS space)?

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It really depends if you are interested in the 2+1 dimensional or the 3+1 dimensional theory.

Under the condition that you mean 3+1 dimensions:

Nonlinear higher spin theories in various dimensions - X. Bekaert, S. Cnockaert, Carlo Iazeolla, M.A. Vasiliev is a standard reference

Elements of Vasiliev theory - V.E. Didenko, E.D. Skvortsov for an introduction

Additionally there is a whole special issue of "Journal of Physics A" that includes reviews (also for 2+1 dimensional Holography (Gaberdiel and Gopakumar) and 2+1 dimensioanl black holes (Ammon et al)): https://iopscience.iop.org/1751-8121/46/21

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