Marsupials and monotremes, the mammals most distantly related to placental mammals, share essentially the same genome but show major variations in chromosome organization and function. Rules established for the mammalian genome by studies of human and mouse do not always apply to these distantly related mammals, and we must make new and more general laws. Some examples are contradictions to our assumption of frequent genome reshuffling in vertebrate evolution, Ohno's Law of X chromosome conservation, the Lyon Hypothesis of X chromosome inactivation, sex chromosome pairing, several explanations of Haldane's Rule, and the theory that mammalian Y chromosome contains a male-specific gene with a direct dominant action on sex determination. Significantly, it is not always the marsupials and monotremes (usually considered the weird mammals) that are exceptional. In many features, it appears that humans and, particularly, mice are the weird mammals that break more general mammalian, or even vertebrate rules.