The link between poor maternal nutrition and suboptimal outcomes in offspring is well established, but underlying mechanisms are not well understood. Modifications to the offspring epigenome are a plausible mechanism for the transmission of intergenerational signals that could extend to effects of paternal nutrition mediated by epigenetic modifications in sperm. The epigenome is extensively remodeled in the early embryo. Attention has therefore focused on the periconceptional period as a time when differences in parental nutrition might influence the establishment of epigenetic marks in offspring. So-called "natural experiments" in The Gambia and elsewhere have highlighted loci that may be especially sensitive to periconceptional nutrition, and some are associated with health-related outcomes in later life. There is speculation that some epigenetic signals could be transmitted across multiple generations, although this would require epigenetic marks to evade epigenetic reprogramming events at conception and in primordial germ cells, and evidence for this is lacking in humans. Effects on child development spanning one or more generations could impose an intergenerational "brake" on a child's growth potential, limiting, for example, the rate at which populations can escape from stunting.