Although most people are right-handed and have language in their left cerebral hemisphere, why that is so, and in particular why about ten per cent of people are left-handed, is far from clear. Multiple theories have been proposed, often with little in the way of empirical support, and sometimes indeed with strong evidence against them, and yet despite that have become modern urban myths, probably due to the symbolic power of right and left. One thinks in particular of ideas of being right-brained or left-brained, of suggestions that left-handedness is due to perinatal brain damage, of claims that left-handers die seven years earlier than right-handers, and of the unfalsifiable ramifications of the byzantine Geschwind-Behan-Galaburda theory. This article looks back over the past fifty years of research on brain asymmetries, exploring the different themes and approaches, sometimes in relation to the author's own work. Taking all of the work together it is probable that cerebral asymmetries are under genetic control, probably with multiple genetic loci, only a few of which are now beginning to be found thanks to very large databases that are becoming available. Other progress is also seen in proper meta-analyses, the use of fMRI for studying multiple functional lateralisations in large number of individuals, fetal ultra-sound for assessing handedness before birth, and fascinating studies of lateralisation in an ever widening range of animal species. With luck the next fifty years will make more progress and show fewer false directions than had much of the work in the previous fifty years.