  The magma ocean concept was first conceived to explain the geology of the
Moon, but hemispherical or global oceans of silicate melt could be a widespread
"lava world" phase of rocky planet accretion, and could persist on planets on
short-period orbits around other stars. The formation and crystallization of
magma oceans could be a defining stage in the assembly of a core, origin of a
crust, initiation of tectonics, and formation of an atmosphere. The last decade
has seen significant advances in our understanding of this phenomenon through
analysis of terrestrial and extraterrestrial samples, planetary missions, and
astronomical observations of exoplanets. This review describes the energetic
basis of magma oceans and lava worlds and the lava lake analogs available for
study on Earth and Io. It provides an overview of evidence for magma oceans
throughout the Solar System and considers the factors that control the rocks
these magma oceans leave behind. It describes research on theoretical and
observed exoplanets that could host extant magma oceans and summarizes efforts
to detect and characterize them. It reviews modeling of the evolution of magma
oceans as a result of crystallization and evaporation, the interaction with the
underlying solid mantle, and the effects of planetary rotation. The review also
considers theoretical investigations on the formation of an atmosphere in
concert with the magma ocean and in response to irradiation from the host star,
and possible end-states. Finally, it describes needs and gaps in our knowledge
and points to future opportunities with new planetary missions and space
telescopes to identify and better characterize lava worlds around nearby stars.
