  We review recent advances in the analytical and numerical modeling of the
star formation rate in molecular clouds and discuss the available observational
constraints. We focus on molecular clouds as the fundamental star formation
sites, rather than on the larger-scale processes that form the clouds and set
their properties. Molecular clouds are shaped into a complex filamentary
structure by supersonic turbulence, with only a small fraction of the cloud
mass channeled into collapsing protostars over a free-fall time of the system.
In recent years, the physics of supersonic turbulence has been widely explored
with computer simulations, leading to statistical models of this fragmentation
process, and to the prediction of the star formation rate as a function of
fundamental physical parameters of molecular clouds, such as the virial
parameter, the rms Mach number, the compressive fraction of the turbulence
driver, and the ratio of gas to magnetic pressure. Infrared space telescopes,
as well as ground-based observatories have provided unprecedented probes of the
filamentary structure of molecular clouds and the location of forming stars
within them.
