  We review the formation and early evolution of the most massive and dense
young stellar clusters, focusing on the role they can play in our understanding
of star and planet formation as a whole. Young massive cluster (YMC) progenitor
clouds in the Galactic Center can accumulate to a high enough density without
forming stars that the initial protostellar densities are close to the final
stellar density. For this to hold in the disk, the time scale to accumulate the
gas to such high densities must be much shorter than the star formation
timescale. Otherwise the gas begins forming stars while it is being accumulated
to high density. The distinction between the formation regimes in the two
environments is consistent with the predictions of environmentally-dependent
density thresholds for star formation. This implies that stars in YMCs of
similar total mass and radius can have formed at widely different initial
protostellar densities. The fact that no systematic variations in fundamental
properties are observed between YMCs in the disk and Galactic Center suggests
stellar mass assembly is not strongly affected by the initial protostellar
density. We review recent theoretical advances and summarize the debate on
three key open questions: the initial (proto)stellar distribution, infant
(im)mortality and age spreads within YMCs. We conclude: the initial
protostellar distribution is likely hierarchical; YMCs likely experienced a
formation history that was dominated by gas exhaustion rather than gas
expulsion; YMCs are dynamically stable from a young age; and YMCs have age
spreads much smaller than their mean age. Finally, we show that it is plausible
that metal-rich globular clusters may have formed in a similar way to YMCs in
nearby galaxies. In summary, the study of YMC formation bridges star/planet
formation in the solar neighborhood to the oldest structures in the local
Universe. [abridged]
