Research related to crop domestication has been transformed by technologies and discoveries in the genome sciences as well as information-related sciences that are providing new tools for bioinformatics and systems' biology. Rapid progress in archaeobotany and ethnobotany are also contributing new knowledge to understanding crop domestication. This sense of rapid progress is encapsulated in this Special Issue, which contains 18 papers by scientists in botanical, crop sciences and related disciplines on the topic of crop domestication. One paper focuses on current themes in the genetics of crop domestication across crops, whereas other papers have a crop or geographic focus. One feature of progress in the sciences related to crop domestication is the availability of well-characterized germplasm resources in the global network of genetic resources centres (genebanks). Germplasm in genebanks is providing research materials for understanding domestication as well as for plant breeding. In this review, we highlight current genetic themes related to crop domestication. Impressive progress in this field in recent years is transforming plant breeding into crop engineering to meet the human need for increased crop yield with the minimum environmental impact - we consider this to be 'super-domestication'. While the time scale of domestication of 10 000 years or less is a very short evolutionary time span, the details emerging of what has happened and what is happening provide a window to see where domestication might - and can - advance in the future.