This chapter provides an extension of the fundamental Evolutionary Algorithms concepts presented earlier. In particular, we examine the population issue by introducing population structures that are non-panmictic, i.e. in which individuals may only interact with a subset of the population. Two main structures are discussed: multipopulations, or islands, and cellular, also called fine-grained, populations. It is shown in theory and by numerical simulations using different test problems that such population topologies may provide advantages with respect to panmictic populations in terms of diversity and convergence, and also that they lend themselves easily to distributed computation.