  In this paper we survey results on the existence of holomorphic embeddings
and immersions of Stein manifolds into complex manifolds. Most results pertain
to proper maps into Stein manifolds. We include a new result saying that every
continuous map $X\to Y$ between Stein manifolds is homotopic to a proper
holomorphic embedding provided that $\mathrm{dim} Y > 2\mathrm{dim}\, X$ and we
allow a homotopic deformation of the Stein structure on $X$.
