Solids that can be prepared only as microcrystal line powders are not suitable for structural investigation using single crystal diffraction techniques, and it is necessary instead to carry out structure determination using powder diffraction data. In this paper, we focus on a direct-space strategy for solving crystal structures directly from powder diffraction data in which a hypersurface based on the powder profile R-factor R-wp is searched using a Genetic Algorithm, and we highlight some recent fundamental developments relating to this methodology.