Understanding the nature of warm dense matter associated with materials at near-solid densities and temperatures of an electron volt or higher remains a challenge to both theory and experiment. Recent enhancements in laser-driven dynamic compression and the laser-heated diamond-anvil cell enable novel experimental studies of materials at high (solid or greater) densities and temperatures at the boundary of the warm dense regime. Experiments on initially-solid insulators such as diamond and magnesium oxide, initially-molecular materials such as nitrogen and hydrogen, and initially-noble gases such as argon will be presented. These studies use a combination of thermodynamic observations (of, for example, temperature) and optical-property measurements (such as reflectivity or absorptivity) to characterize solid-solid phase transformations at electron-volt temperatures, melting at high pressure, and electronic transformations at the boundary of the warm dense regime.