Invited review abstract

I will present results from AMR and SPH simulations of the gravitational
fragmentation of ballistically-expanding shells in which we explored the
effects of the boundary conditions on the fragmentation, and of subsequent
accretion on the final mass function. I will then present simulations of
the external irradiation of a turbulent molecular cloud in which I study
the effects of triggering on the stellar mass function and star formation
efficiency. I will then discuss the implications of all this work for
triggered star formation, from both observational and theoretical points
of view.