The majority of stars are now thought to support exoplanets. Many of those exoplanets discovered thus far are categorized as rocky objects with an atmosphere. Most of these objects are however hot due to their short orbital period. Models suggest that water is the dominant species in their atmospheres. The hot temperatures are expected to turn these atmospheres into a (high pressure) steam bath containing remains of melted rock. The spectroscopy of these hot rocky objects will be very different from that of cooler objects or hot gas giants. Molecules suggested to be important for the spectroscopy of these objects are reviewed together with the current status of the corresponding spectroscopic data. Perspectives of building a comprehensive database of linelist/cross sections applicable for atmospheric models of rocky super-Earths as part of the ExoMol project are discussed.The quantum-mechanical approaches used in linelist productions and their challenges are summarized. ), key hot exoplanets with masses and radii in the rocky-planet range includeCoRoT-7b, Kepler-10b, Kepler-78b, Kepler-97b, Kepler-99b, Kepler-102b, Kepler-93b being slightly cooler than 1673 K [21,22,30,31,32,33,34,35,36] Most of the rocky exoplanets that have so far been studied are characterized by the high temperature of their atmospheres, e.g., about 1500 K in Kepler-36b and Kepler-93b, 2474 ± 71 K in CoRoT-7b [37], 2360 ± 300 K in 55 Cnc