After briefly reviewing the progress that has been made in using the
methods of integrable systems to compute the spectrum of planar N=4
gauge theory, I will discuss various ways in which integrable models
with boundaries enter the picture. In particular, I will discuss
boundary conditions arising from the addition of fundamental matter to
the gauge theory. Finally, I will argue that the open-boundaries setup
provides a useful laboratory for testing ideas about finite-size
effects, which have been the subject of much recent interest.