The statement that primates and humans are the only mammals who menstruate is only partly true. Also bats and elephant shrews get their periods.
In some aspects, the cycle of all mammals is the same: the endometrium thickens in preparation for the implantation of the embryo. If the egg isn’t fertilised, the endometrium lining is shed again. However, in most mammals the lining is so thin; it’s completely reabsorbed into the body. This is called covert menstruation.
In others, like humans, the endometrial lining is thicker and part of it leaves the body through the vagina, which is called overt menstruation. This happens to humans and to almost all the African and Asiatic monkeys, together about 50 different species. Only a few species of the monkeys are known to have overt menstruation. Also non-primates menstruate this way, like African elephant shrews, tree shrews (or tupaia) and four different bat species.
What differs us from monkeys, is that female humans get their menopause around the age of 50. Female chimpanzees – who reach an average age of 50 – menstruate and ovulate until the day they die and can still get pregnant when they’re 50. Another difference: ape’s bottoms swell and shrink on the rhythm of their cycles, signalling their fertile periods.
Why female humans usually outlive their fertility by decades is unknown. One hypothesis is that grandparents play an important role in the human society, as human babies are very helpless and depend on their carers for a long time. This way, the extra support given by grandparents could be the key to the success of humankind.