Magma oceans are a common result of the high degree of heating that occurs during planet formation. It is thought that almost all of the large rocky bodies in the Solar System went through at least one magma ocean phase. In this paper, we review some of the ways in which magma ocean models for the Earth, Moon and Mars match present-day observations of mantle reservoirs, internal structure and primordial crusts, and then we present new calculations for the oxidation state of the mantle produced during the magma ocean phase. The crystallization of magma oceans probably leads to a massive mantle overturn that may set up a stably stratified mantle. This may lead to significant delays or total prevention of plate tectonics on some planets. We review recent models that may help partly alleviate the mantle stability and lead to earlier onset of plate tectonics.This article is part of a discussion meeting issue ‘Earth dynamics and the development of plate tectonics’.