The first specimen of platypus (Ornithorhynchus anatinus) that reached Britain in the late 18th century was regarded a scientific hoax. Over decades the anatomical characteristics of these unique mammals, such as egg laying and the existence of mammary glands, were hotly debated before they were accepted. Within the last 40 years, more and more details of monotreme physiology, histology, reproduction and genetics have been revealed. Some show similarities with birds or reptiles, some with therian mammals, but many are very specific to monotremes. The genome is no exception to monotreme uniqueness. An early opinion was that the karyotype, composed of a few large chromosomes and many small ones, resembled bird and reptile macro- and micro-chromosomes. However, the platypus genome also features characteristics that are not present in other mammals, such as a complex translocation system. The sex chromosome system is still not resolved. Nothing is known about dosage compensation and, unlike in therian mammals, there seems to be no genomic imprinting. In this article we will recount the mysteries of the monotreme genome and describe how we are using recently developed technology to identify chromosomes in mitosis, meiosis and sperm, to map genes to chromosomes, to unravel the sex chromosome system and the translocation chain and investigate X inactivation and genomic imprinting in monotremes.