Basal magma oceans develop in Earth and Venus after accretion as their mantles solidify from the middle outwards. Fractional crystallization of the basal mantle is buffered by the core and radiogenic and latent heat in the magma ocean. Previous studies showed that Earth’s basal magma ocean would have solidified after two or three billion years. Venus has a relatively hot interior that cools slowly in the absence of plate tectonics, which reduces heat flow through the solid mantle. Consequentially, the basal magma ocean could remain as thick as ~200-400 km today. Vigorous convection of liquid silicates could power a global magnetic field until recently while a core-hosted dynamo is suppressed. The basal magma ocean may be a hidden reservoir of potassium and other incompatible elements. A high tidal Love number could reveal a basal magma ocean and would definitively establish that the core is at least partially liquid.