  The link between a particular class of growth processes and random matrices
was established in the now famous 1999 article of Baik, Deift, and Johansson on
the length of the longest increasing subsequence of a random permutation.
During the past ten years, this connection has been worked out in detail and
led to an improved understanding of the large scale properties of
one-dimensional growth models. The reader will find a commented list of
references at the end. Our objective is to provide an introduction highlighting
random matrices. From the outset it should be emphasized that this connection
is fragile. Only certain aspects, and only for specific models, the growth
process can be reexpressed in terms of partition functions also appearing in
random matrix theory.
