B chromosomes (Bs) can be described as 'passengers in the genome', a term that has been used for the repetitive DNA which comprises the bulk of the genome in large genome species, except that Bs have a life of their own as independent chromosomes. As with retrotransposons they can accumulate in number, but in this case by various processes of mitotic or meiotic drive, based on their own autonomous ways of using spindles, especially in the gametophyte phase of the life cycle of flowering plants. This selfish property of drive ensures their survival and spread in natural populations, even against a gradient of harmful effects on the host plant phenotype. Bs are inhabitants of the nucleus and they are subject to control by 'genes' in the A chromosome (As) complement. This interaction with the As, together with the balance between drive and harmful effects makes a dynamic system in the life of a B chromosome, notwithstanding the fact that we are only now beginning to unravel the story in a few favoured species. In this review we concentrate mainly on recent developments in the Bs of rye and maize, two of the species currently receiving most attention. We focus on their population dynamics and on the molecular basis of their structural organisation and mechanisms of drive, as well as on their mode of origin and potential applications in plant biotechnology.