  In this chapter I review theoretical models for the formation of very massive
stars. After a brief overview of some relevant observations, I spend the bulk
of the chapter describing two possible routes to the formation of very massive
stars: formation via gas accretion, and formation via collisions between
smaller stars. For direct accretion, I discuss the problems of how interstellar
gas may be prevented from fragmenting so that it is available for incorporation
into a single very massive star, and I discuss the problems presented for
massive star formation by feedback in the form of radiation pressure,
photoionization, and stellar winds. For collision, I discuss several mechanisms
by which stars might be induced to collide, and I discuss what sorts of
environments are required to enable each of these mechanisms to function. I
then compare the direct accretion and collision scenarios, and discuss possible
observational signatures that could be used to distinguish between them.
Finally, I come to the question of whether the process of star formation sets
any upper limits on the masses of stars that can form.
