The paper contains a survey of results in the theory of projections: a classification of simple projections of surfaces onto manifolds of low dimension is presented, assertions are formulated regarding the homotopy type of complements to bifurcation diagrams of projections onto a line as are theorems on rectification of vector fields in bundles in a neighborhood of manifolds with singularities, and the connection of the theory of projections with other areas of the theory of singularities (critical points of functions on a smooth manifold and on a manifold with boundary) is considered.