To facilitate the restoration of disturbed vegetation, seeds of wild species are collected and held in dry storage, but often there is a shortage of seeds for this purpose. Thus, much research effort is expended to maximize the use of the available seeds and to ensure that they are nondormant when sown. Sowing nondormant (versus dormant) seeds in the field should increase the success of the restoration. Of the various treatments available to break seed dormancy, afterripening, that is, dormancy break during dry storage, is the most cost-effective. Seeds that can undergo afterripening have nondeep physiological dormancy, and this includes members of common families such as Asteraceae and Poaceae. In this review, we consider differences between species in terms of seed moisture content, temperature and time required for afterripening and discuss the conditions in which afterripening is rapid but could lead to seed aging and death if storage is too long. Attention is given to the induction of secondary dormancy in seeds that have become nondormant via afterripening and to the biochemical and molecular changes occurring in seeds during dry storage. Some recommendations are made for managing afterripening so that seeds are nondormant at the time for sowing. The most important recommendation probably is that germination responses of the seeds need to be monitored for germinability/viability during the storage period.