How best to analyse and describe the features of the situation commonly known as "visceral heterotaxy" remains controversial. Much of the disagreement devolves on how to deal with the concept of isomerism. In the opinion of some, the concept of bilateral right-sidedness and bilateral left-sidedness, while useful in helping to remember which abnormalities are likely to occur in asplenia or polysplenia, should not be granted the status of a specific "situs", since there are numerous examples of exceptions to these patterns. On the other hand, those who favour the concept of isomerism point out that, when describing only the heart, and taking the structure of the atrial appendages as the starting point for analysis, basing this on the extent of the pectinate muscles relative to the atrioventricular junctions, then the only possible arrangements for the appendages are the usual one, its mirror-image, and the two situations in which appendages of comparable morphology are found on both sides of the heart, these being the arrangements of right or left isomerism. It is certainly the case that the arrangement of the organs is not always in harmony with the arrangement of the atrial appendages, but those circumstances, in which there is disharmony, can readily be described by paying specific attention to each series of organs. On this basis, in this review, we describe the approach to heterotaxy, and isomerism of the atrial appendages, in terms of the genetic background, the diagnosis, and outcomes after cardiac surgery. Attention is given to the various diagnostic modalities, including fetal and postnatal echocardiography, recent tomographic and magnetic resonance imaging techniques, and the time-honoured approach using angiography.