It is timely to re-examine the phenomenon of polyploidy in plants. Indeed, the power of modern molecular technology to provide new insights, and the impetus of genomics, make polyploidy a fit, fashionable and futuristic topic for review. Some historical perspective is essential to understand the meaning of the terms, to recognize what is already known and what is dogma, and to frame incisive questions for future research. Polyploidy is important because life on earth is predominantly a polyploid phenomenon. Moreover, civilization is mainly powered by polyploid food – notably cereal endosperm. Ongoing uncertainty about the origin of triploid endosperm epitomizes our ignorance about somatic polyploidy. New molecular information makes it timely to reconsider how to identity polyploids and what is a polyploid state. A functional definition in terms of a minimal genome may be helpful. Genes are known that can raise or lower ploidy level. Molecular studies can test if, contrary to dogma, the relationship between diploids and polyploids is a dynamic two-way system. We still need to understand the mechanisms and roles of key genes controlling ploidy level and disomic inheritance. New evidence for genome duplications should be compared with old ideas about cryptopolyploidy, and new views of meiosis should not ignore premeiotic genome separation. In practice, new knowledge about polyploidy will be most useful only when it reliably predicts which crops can be usefully improved as stable autopolyploids and which genomes combined to create successful new allopolyloids. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 82, 411–423.