In this review the frame-like formulation of massless gauge fields of any spin propagating in Minkowski and (anti-)de Sitter spaces of any dimension is discussed. The notions of higher-spin gauge fields, gauge symmetries, and gauge-invariant field strengths are introduced in the framework of the frame-like description. The general building procedure for the gauge-invariant action functionals for free higher-spin fields is discussed. Also, several substantial examples of actions for fields of particular spins are considered. The proposed frame-like formulation represents the effective tool for constructing interactions of higher-spin fields on the AdS background. As a case in point, non-linear AdS₅ = 1 SUSY higher-spin gauge theory on the level of the cubic action functional describing interactions of massless higher-spin fields between themselves and gravity is constructed.

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