Understanding the evolutionary plasticity of the genome requires a global, comparative approach in which genetic events are considered both in a phylogenetic framework and with regard to population genetics and environmental variables. In the mechanisms that generate adaptive and non-adaptive changes in genomes, segmental duplications (duplication of individual genes or genomic regions) and polyploidization (whole genome duplications) are well-known driving forces. The probability of fixation and maintenance of duplicates depends on many variables, including population sizes and selection regimes experienced by the corresponding genes: a combination of stochastic and adaptive mechanisms has shaped all genomes. A survey of experimental work shows that the distinction made between fixation and maintenance of duplicates still needs to be conceptualized and mathematically modeled. Here we review the mechanisms that increase or decrease the probability of fixation or maintenance of duplicated genes, and examine the outcome of these events on the adaptation of the organisms.