Polyploidy or whole genome duplication (WGD) is an evolutionary phenomenon that happened in all angiosperms multiple times over millions of years. Extensive studies on the model plant Arabidopsis thaliana genome have revealed that it has undergone five rounds of WGDs followed, in the Brassicaceae tribe, by a characteristic whole genome triplication (WGT). In addition, small-scale events such as tandem or segmental duplications and retrotransposition also enable plants to reshape their genomes. Over the decades, extensive research efforts have been undertaken to understand the evolutionary significance of polyploidy. On the other hand, much less attention has been paid to understanding the impact of gene duplication on the diversification of important stress response genes. The main objective of this review is to discuss key aspects of gene and genome duplications with a focus on genes primarily regulated by osmotic stresses. The focal family is the Brassicaceae, since it (i) underwent multiple rounds of WGDs plus WGTs, (ii) hosts many economically important crops and wild relatives that are tolerant to a range of stresses, and (iii) comprises many species that have already been sequenced. Diverse molecular mechanisms that lead to structural and regulatory alterations of duplicated genes are discussed. Examples are drawn from recent literature to elucidate expanded, stress responsive gene families identified from different Brassica crops. A combined bioinformatic and transcriptomic method has been proposed and tested on a known stress-responsive gene pair to prove that stress-responsive duplicated allelic variants can be identified by this method. Finally, future prospects for engineering these genes into crops to enhance stress tolerance are discussed, and important resources for Brassica genome research are provided.