Maize weevil (Sitophilus zeamais) causes extensive damage to stored maize (Zea mays), particularly to grain stored on-farm without chemical protectants.  Breeding of maize varieties with improved weevil resistance, however, is not practiced to any significant extent, because of uncertain probability of success and because seed producers generally consider storability of grain to be outside of their responsibility.  The Rockefeller Foundation-funded Weevil Project, at CIMMYT, has guided a total of four graduate students through a progression of studies investigating the genetics of weevil resistance and exploring practical methods for breeding maize with increased resistance to weevil.  Important milestones within the five years of the project have been: 1) Identification of significant genetic variation for weevil resistance among regionally-adapted maize germplasm, 2) Investigations of secondary traits for use in selecting maize with weevil resistance, 3) Successful divergent selection for weevil resistance in several maize populations, and 4) Ongoing investigations of per se resistance relative to hybrid performance for maize lines at various levels of inbreeding.  This paper will summarize recent results, describe on-going work, and offer recommendations based on our current understanding of this important challenge.  It is clear from results to date that breeding for improved weevil resistance is possible; it remains unclear, however, what breeding method(s), if any, are practical, effective and feasible for widespread use in maize breeding programs.