Understanding the quantitative genetics of crops has been and will continue to be central to maintaining and improving global food security. We outline four stages that plant breeding either has already achieved or will probably soon achieve. Top-of-the-line breeding programs are currently in Breeding 3.0, where inexpensive, genome-wide data coupled with powerful algorithms allow us to start breeding on predicted instead of measured phenotypes. We focus on three major questions that must be answered to move from current Breeding 3.0 practices to Breeding 4.0: (a) How do we adapt crops to better fit agricultural environments? (b) What is the nature of the diversity upon which breeding can act? (c) How do we deal with deleterious variants? Answering these questions and then translating them to actual gains for farmers will be a significant part of achieving global food security in the twenty-first century.

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