Whether or not molecular clouds and embedded cloud fragments are stable against collapse is of utmost importance for the study of the star formation process. Only supercritical cloud fragments are able to collapse and form stars. The virial parameter, alpha=M_vir/M, which compares the virial to the actual mass, provides one way to gauge stability against collapse. Supercritical cloud fragments are characterized by alpha<2, as indicated by a comprehensive stability analysis considering perturbations in pressure and density gradients. Past research has suggested that virial parameters alpha>2 prevail in clouds. This would suggest that collapse towards star formation is a gradual and relatively slow process, and that magnetic fields are not needed to explain the observed cloud structure. Here, we review a range of very recent observational studies that derive virial parameters <<2 and compile a catalogue of 1325 virial parameter estimates. Low values of alpha are in particular observed for regions of high mass star formation (HMSF). These observations may argue for a more rapid and violent evolution during collapse. This would enable competitive accretion in HMSF, constrain some models of monolithic collapse, and might explain the absence of high--mass starless cores. Alternatively, the data could point at the presence of significant magnetic fields ~1 mG at high gas densities. We examine to what extent the derived observational properties might be biased by observational or theoretical uncertainties. For a wide range of reasonable parameters, our conclusions appear to be robust with respect to such biases.
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