Kinship, diverse webs of relationship generated by people in their social practice, has long been analysed and debated by anthropologists, from an earlier dominance of lineage theory to the current, much more fluid emphasis on relatedness. Since the days of processualism, archaeologists have given more attention to kinship than in the early years of the discipline, but in rather limited and general ways until very recently. With the advent of successful aDNA investigations, and with some prompt from posthumanist theory, that interest has been renewed recently. I discuss some inconsistencies between the accounts of kinship by anthropologists and archaeologists, notably the emphasis by the former on diversity, relatedness, the possibilities and implications of bilateral descent, and the uncertain relationship between biology and kinship. To begin to investigate how this might all work out in archaeology, I sketch three scenarios from successive parts of the Neolithic in Britain and Ireland, across the fourth to third millennia cal BC, attempting specific rather than generalised models and indicating the outlines of a possible trajectory through time.