Although single crystal X-ray diffraction is a powerful technique for the determination of crystal and molecular structures, many solids can be prepared only as microcrystalline powders and therefore cannot be studied by single crystal diffraction techniques. For such materials, it is necessary to tackle structure determination using powder diffraction data. This article highlights recent developments in the opportunities for determining the crystal structures of molecular solids directly from powder diffraction data, focusing on the challenging structure solution stage of the structure determination process. In particular, the direct-space strategy for structure solution is highlighted, as this approach has led to significant recent advances in the structure determination of molecular solids. In the direct-space approach, a hypersurface defined by an appropriate powder diffraction R-factor is explored using global optimization techniques, and we focus on our development and application of Monte Carlo and genetic algorithm techniques within this field. Fundamental aspects are described, and examples are given to illustrate the application of the direct-space strategy to determine crystal structures of molecular materials.