Some of the challenges facing scientists in the area of the electronic structure and properties of solids are reviewed. At a time when computational advances have made possible high-quality calculations, not even conceivable 10 years ago, the article stresses the importance of going beyond the raw output of the calculation and understanding where the result originates. The areas selected for study include the Fermi surface and charge density waves, the stability of solids and the structures of solids under pressure, metal-insulator transitions, the method of moments, superconductivity, and the use of a relatively new technique for the study of chemical bonding, the electron localization function (ELF).