  The phenomenon of protein synthesis has been modeled in terms of totally
asymmetric simple exclusion processes (TASEP) since 1968. In this article, we
provide a tutorial of the biological and mathematical aspects of this approach.
We also summarize several new results, concerned with limited resources in the
cell and simple estimates for the current (protein production rate) of a TASEP
with inhomogeneous hopping rates, reflecting the characteristics of real genes.
