We review the properties of low mass dense molecular cloud cores, including starless, prestellar, and Class 0 protostellar cores, as derived from observations. In particular we discuss them in the context of the current debate surrounding the formation and evolution of cores. There exist several families of model scenarios to explain this evolution (with many variations of each) that can be thought of as a continuum of models lying between two extreme paradigms for the star and core formation process. At one extreme there is the dynamic, turbulent picture, while at the other extreme there is a slow, quasi-static vision of core evolution. In the latter view the magnetic field plays a dominant role, and it may also play some role in the former picture. Polarization and Zeeman measurements indicate that some, if not all, cores contain a significant magnetic field. Wide-field surveys constrain the timescales of the core formation and evolution processes, as well as the statistical distribution of core masses. The former indicates that prestellar cores typically live for 2--5 free-fall times, while the latter seems to determine the stellar initial mass function. In addition, multiple surveys allow one to compare core properties in different regions. From this it appears that aspects of different models may be relevant to different star-forming regions, depending on the environment. Prestellar cores in cluster-forming regions are smaller in radius and have higher column densities, by up to an order of magnitude, than isolated prestellar cores. This is probably due to the fact that in cluster-forming regions the prestellar cores are formed by fragmentation of larger, more turbulent cluster-forming cores, which in turn form as a result of strong external compression.
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