  In this paper we expose the impact of the fundamental discovery, made by Erik
Anders\'en and L\'aszl\'o Lempert in 1992, that the group generated by shears
is dense in the group of holomorphic automorphisms of complex Euclidean spaces
of dimensions $n>1$. In three decades since its publication, their
groundbreaking work led to the discovery of several new phenomena and to major
new results in complex analysis and geometry involving Stein manifolds and
affine algebraic manifolds with many automorphisms. The aim of this survey is
to present some focal points of these developments, with a view towards the
future.
