  Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of
much theoretical interest for more than two decades. They are in particular
important for the analysis and interpretation of QCD simulations on a finite,
discrete space-time lattice. Most of these effects are closely related to the
phenomenon of spontaneous breaking of the chiral flavor symmetry and the
emergence of pions as light Goldstone bosons. These long-range fluctuations are
strongly affected by putting the system into a finite box, and an analysis with
different methods can be organized according to the interplay between pion mass
and box size. The finite volume also affects critical behavior at the chiral
phase transition in QCD. In the present review, I will be mainly concerned with
modeling such finite volume effects as they affect the thermodynamics of the
chiral phase transition for two quark flavors.
  I review recent work on the analysis of finite-volume effects which makes use
of the quark-meson model for dynamical chiral symmetry breaking. To account for
the effects of critical long-range fluctuations close to the phase transition,
most of the calculations have been performed using non-perturbative
Renormalization Group (RG) methods. I give an overview over the application of
these methods to a finite volume. The method, the model and the results are put
into the context of related work in random matrix theory for very small
volumes, chiral perturbation theory for larger volumes, and related methods and
approaches. They are applied towards the analysis of finite-volume effects in
lattice QCD simulations and their interpretation, mainly in the context of the
chiral phase transition for two quark flavors.
