  Numerical simulations of star cluster formation have advanced greatly during
the past decade, covering increasingly massive gas clouds while accounting for
more and more complex physics. In this review, I discuss the present state of
the field, paying particular attention to the key physics that need to be
included in cluster formation simulations. The main numerical techniques are
summarized for a broad audience, before evaluating their application to the
problem of cluster formation. A faithful reproduction of the observed
characteristics of cluster formation can presently be achieved in numerical
simulations. Ideally, this requires turbulent initial conditions to be combined
with radiative feedback, protostellar outflows, and magnetic fields. With the
exciting prospect in mind that our understanding of cluster formation will soon
be revolutionized by facilities like ALMA, JWST, and the EVLA, this review also
identifies a number of areas that would particularly benefit from a joint
observational and theoretical effort.
