Stars are born in turbulent, magnetized filamentary molecular clouds, typically as members of star clusters. Several remarkable technical advances enable observations of magnetic structure and field strengths across many physical scales, from galactic scales on which giant molecular clouds (GMCs) are assembled, down to the surfaces of magnetized accreting young stars. These are shedding new light on the role of magnetic fields in star formation. Magnetic fields affect the gravitational fragmentation and formation of filamentary molecular clouds, the formation and fragmentation of magnetized disks, and finally to the shedding of excess angular momentum in jets and outflows from both the disks and young stars. Magnetic fields play a particularly important role in angular momentum transport on all of these scales. Numerical simulations have provided an important tool for tracking the complex process of the collapse and evolution of protostellar gas since several competing physical processes are at play - turbulence, gravity, MHD, and radiation fields. This paper focuses on the role of magnetic fields in three crucial regimes of star formation: the formation of star clusters emphasizing fragmentation, disk formation and the origin of early jets and outflows, to processes that control the spin evolution of young stars.