  Given a nonnegative matrix $A$, can you find diagonal matrices $D_1,~D_2$
such that $D_1AD_2$ is doubly stochastic? The answer to this question is known
as Sinkhorn's theorem. It has been proved with a wide variety of methods, each
presenting a variety of possible generalisations. Recently, generalisations
such as to positive maps between matrix algebras have become more and more
interesting for applications. This text gives a review of over 70 years of
matrix scaling. The focus lies on the mathematical landscape surrounding the
problem and its solution as well as the generalisation to positive maps and
contains hardly any nontrivial unpublished results.
