Structural topology optimization is addressed through Genetic Algorithms: A set of designs is evolved following the Darwinian survival-of-fittest principle. The goal is to optimize the weight of the structure under displacement constraints. This approach demonstrates high flexibility, and breaks many limits of standard optimization algorithms, in spite of the heavy requirements in term of computational effort: Alternate optimal solutions to the same problem can be found; Structures can be optimized with respect to multiple loadings; The prescribed loadings can be applied on the unknown boundary of the solution, rather than on the fixed boundary of the design domain; Different materials as well as different mechanical models can be used, as witnessed by the first results of Topological Optimum Design ever obtained in the large displacements model. But these results could not have been obtained without careful specific handling of the specific aspects of topological genetic optimization: First, specific genetic operators (crossover, mutation) were introduced; Second, special attention was paid to the design of the objective function; The nonlinear geometrical effects of the large displacement model lead to non viable solutions, unless some constraints are imposed on the stress field.