Aiming at non-experts, we explain the key mechanisms of higher-spin
extensions of ordinary gravity. We first overview various no-go theorems for
low-energy scattering of massless particles in flat spacetime. In doing so we
dress a dictionary between the S-matrix and the Lagrangian approaches,
exhibiting their relative advantages and weaknesses, after which we high-light
potential loop-holes for non-trivial massless dynamics. We then review positive
yes-go results for non-abelian cubic higher-derivative vertices in constantly
curved backgrounds. Finally we outline how higher-spin symmetry can be
reconciled with the equivalence principle in the presence of a cosmological
constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin
gravity with its double perturbative expansion (in terms of numbers of fields
and derivatives).Comment: LaTeX, 50 pages, minor changes, many refs added; version accepted for
publication in Reviews of Modern Physic
