Seeds are central to crop production, human nutrition, and food security. A key component of the performance of crop seeds is the complex trait of seed vigour. Crop yield and resource use efficiency depend on successful plant establishment in the field, and it is the vigour of seeds that defines their ability to germinate and establish seedlings rapidly, uniformly, and robustly across diverse environmental conditions. Improving vigour to enhance the critical and yield-defining stage of crop establishment remains a primary objective of the agricultural industry and the seed/breeding companies that support it. Our knowledge of the regulation of seed germination has developed greatly in recent times, yet understanding of the basis of variation in vigour and therefore seed performance during the establishment of crops remains limited. Here we consider seed vigour at an ecophysiological, molecular, and biomechanical level. We discuss how some seed characteristics that serve as adaptive responses to the natural environment are not suitable for agriculture. Past domestication has provided incremental improvements, but further actively directed change is required to produce seeds with the characteristics required both now and in the future. We discuss ways in which basic plant science could be applied to enhance seed performance in crop production.