The currently available empirical evidence on the star formation processes in the extreme, high-pressure environments induced by galaxy encounters, mostly based on high-resolution Hubble Space Telescope imaging observations, strongly suggests that star cluster formation is an important and perhaps even the dominant mode of star formation in the starburst events associated with galaxy interactions. The production of young massive star clusters (YSCs) seems to be a hallmark of intense star formation, particularly in interacting and starburst galaxies. Their sizes, luminosities, and mass estimates are entirely consistent with what is expected for young Milky Way-type globular clusters (GCs). YSCs are important because of what they can tell us about GC formation and evolution (e.g., initial characteristics and early survival rates). They are also of prime importance as probes of the formation and (chemical) evolution of their host galaxies, and of the initial mass function in the extreme environments required for cluster formation. Recent evidence lends support to the scenario that Milky Way-type GCs (although more metal rich), which were once thought to be the oldest building blocks of galaxies, are still forming today.