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Although the basic physics of star formation is classical, numerical simulations have yielded essential insights into how stars form. They show that star formation is a highly nonuniform runaway process characterized by the emergence of nearly singular peaks in density, followed by the accretional growth of embryo stars that form at these density peaks. Circumstellar discs often form from the gas being accreted by the forming stars, and accretion from these discs may be episodic, driven by gravitational instabilities or by protostellar interactions. Star-forming clouds typically develop filamentary structures, which may, along with the thermal physics, play an important role in the origin of stellar masses because of the sensitivity of filament fragmentation to temperature variations. Simulations of the formation of star clusters show that the most massive stars form by continuing accretion in the dense cluster cores, and this again is a runaway process that couples star formation and cluster formation. Star-forming clouds also tend to develop hierarchical structures, and smaller groups of forming objects tend to merge into progressively larger ones, a generic feature of self-gravitating systems that is common to star formation and galaxy formation. Because of the large range of scales and the complex dynamics involved, analytic models cannot adequately describe many aspects of star formation, and detailed numerical simulations are needed to advance our understanding of the subject. ‘The purpose of computing is insight, not numbers.’ Richard W Hamming, in Numerical Methods for Scientists and Engineers (1962) ‘There are more things in heaven and earth, Horatio