This conference will address the science of planetary interiors by combining recent observations of exoplanets, advances in planetary orbital dynamics, and discoveries in experimental and theoretical high pressure science. An emphasis will be placed on planets with radii up to 2.5 times that of the Earth.This conference is intended to synthesize recent advances from astrophysics and geophysics to advance our understanding of the composition, structure, and evolution of rocky planets. The discovery of such primarily rocky, super-Earth planets beyond the solar system is rapidly expanding the scope of traditional interior geophysics. The diverse interiors, atmospheres with varying amounts of gas and volatile elements, and potential oceans on such planets spawn broader questions about their formation, including the physics of protoplanetary disks, the accumulation of refractory material, the dynamical interactions of embryonic rocky bodies and gas, and the build-up of rocky planets with associated lighter material. New astronomical observations, such as measurements of radii and masses of nearly Earth-size planets, transit-timing variations, orbital resonances, the Rossiter-McLaughlin effect, and the frequency of planets as a function of size, orbital properties, and stellar host properties, are now informing the physics of planet formation and providing the boundary conditions that constrain the interior structures of rocky planets. New laboratory measurements using diamond anvil cells and shock wave experiments can access an extended range of pressure and temperature conditions. Ab initio simulations enable us to characterize planetary materials over the entire range of conditions in the interiors of exoplanets. Combining theory with experimental results enable us to construct more realistic models of exoplanet interiors. Advances in computational methods for simulating large-scale convection allow us to characterize their thermal structure and evolution.