Of the four terrestrial planets in our solar system, two support CO2-N2-rich atmospheres, one is airless, and the other, the Earth, is remarkable for the presence of O2. Yet it is unclear as to the underlying pathways by which these atmospheres were formed. How common are such atmospheres on planets orbiting other stars? To what extent do they reflect the material from which the planets accreted? Our ability to now interrogate the compositions of exoplanetary atmospheres via spectroscopic means has afforded us the possibility to address these questions. Here, we examine how experiments are used to determine the extent and nature of mass exchange between the interior and atmosphere. The solubilities of the major atmosphere-forming gases in silicate liquids result in C-rich (as opposed to H-rich) atmospheres unless the planets are highly reduced, while S-rich atmospheres emerge under moderately oxidising redox conditions. Coupling the equilibrium partial pressures of the prevailing gases with their opacities permits computation of the radiative properties of the atmosphere. Forward-modelling of atmospheric spectra around lava ocean worlds, observable by the James Webb Space Telescope, indicates that even close-in exoplanets can harbour H-rich atmospheres. This supports the notion that rocky planets may have initially formed in the presence of the nebular gas.