  I review some recent work on low-mass star formation, with an emphasis on
theory, basic principles, and unresolved questions. Star formation is both a
gravitational fragmentation problem as well as an accretion problem. Molecular
cloud structure can be understood as a fragmentation process driven by the
interplay of turbulence, magnetic fields, and gravity (acting on either a
dynamical or ambipolar-diffusion time scale). This results in a natural way to
understand filamentary structure as magnetic ribbons that have an apparent
width that scales differently than the Jeans length. Recent work also shows
that stellar mass accretion through a disk is episodic. We show through
numerical simulations that bursts of FU Ori type may be clustered, since the
clump that accretes to the center is tidally sheared apart in its last stage of
infall. Finally, we utilize a simplified model of stellar mass accretion and
accretion termination to derive an analytic form for the initial mass function
that has a lognormal-like body and a power-law tail. This scenario is
consistent with an expectation of a larger number of substellar objects than
may have been previously detected.
