The background and use of dual-space direct methods for the ab initio phasing of small macromolecules as well as the phasing of heavy-atom substructures of larger biological structures are described. Basic concepts include normalized structure factors, multisolution procedures, random trial structures, phase-refinement formulas, peak-picking techniques, density modification including charge flipping, and recognizing solutions. Other topics discussed are the use of Patterson information to get better starting phases, avoiding false minima, the effects of data resolution, data quality and completeness, special features of space group P1, refinement strategies, and future possibilities. Several independent computer programs that implement these concepts are then briefly described.
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