  This is a survey on the homotopy principle in complex analysis on Stein
manifolds, also called the Oka principle in this context. We concentrate on the
following topics: the Oka-Grauert principle (classification of holomorphic
vector bundles); the homotopy principle for holomorphic mappings from Stein
manifolds and, more generally, for sections of holomorphic submersions with
sprays; question on removability of intersections of holomorphic mappings with
complex subvarieties; embeddings and immersions of Stein manifolds in affine
spaces of minimal dimension; embeddings of open Riemann surfaces in the affine
plane; noncritical holomorphic functions on Stein manifolds and the Oka
principle for holomorphic submersions of Stein manifolds to affine spaces.
