Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations, and for better conservation and management of natural resources such as fish stocks. In this review we focus on the impact of random sweepstakes on selection in highly fecund populations. In random sweepstakes the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. We also describe selective sweepstakes which are well approximated by recurrent selective sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation. Finally, we review an important case study in which a model of recurrent selective sweeps is shown to essentially explain population genomic data of the highly fecund Atlantic cod, with broad implications for studying the evolution and ecology of highly fecund populations across domains of life.