Their cousin called monotreme
The platypus is one of two surviving types of creature called monotremes, which, in case you were unaware, are kind of marsupials plus, or maybe minus. They have fur, and some of them sometimes have pouches in which their young develop, but they also lay eggs and have bills, sort of like birds, and in the case of male platypuses poisonous ankles also. They also have teeth, but only when young. The platypus is the famous monotreme; less well known for some reason (though even weirder in my opinion) is the echidna, also known more descriptively as the spiny anteater. Together, they are the only surviving examples of the oldest mammals ever to exist. Echidnas and platypuses, as well as several extinct species of monotreme, shared the Earth with the dinosaurs.
Monotremes are really weird. Everything about them seems to have been thought up past some kind of deadline. Take the method by which they reproduce: after mating, the female lays an egg (echidna) or two (platypus). Then she carries them around until they hatch. Monotremes are mammalian, even if what they have is a kind of free demo version of mammalianism without the really useful features like live birth, so they lactate. But they have no nipples. The milk just leaks right out of glands in their skin, and the baby monotreme laps it up with sweeps of its tiny bill. (A baby echidna is called a puggle. There is no official name for a baby platypus, though "platypup" has been suggested.) The platypus doesn't even have a pouch, so after the eggs hatch -- after the female has incubated them by pressing them to her belly with her tail -- the babies must lap up these rivulets of milk while clinging to her fur for dear life.
Not that having a pouch simplifies the process any. The echidna (which comes in three varieties, short-beaked, long-beaked, and cyclops long-beaked) doesn't usually have a pouch but grows one as necessary. After mating there is a gestation period of about three weeks, and then the female lies down on her back, doubles over, and lays her egg right into her own temporary pouch. After a while the egg hatches in the pouch. And echidnas are covered with aggressive spines, which adds a new wrinkle, as the mother cannot carry her puggle once these start to develop. So she buries it. (Echidnas are good diggers; if you startle one it will sink as if by magic into the ground until only its spines are exposed. In this position it is all but unassailable.) Alternately, she hides it under a bush. Every five to ten days she unburies it and lets it nurse for a while before burying it again. Keep in mind that the puggle, like a joey, is still somewhat fetal while this is going on. It's a half-fetus half-baby thing buried in the dirt.
The echidna is therefore "born" three times -- once as an egg, once when the egg hatches, and once when the puggle is evicted from the pouch and hidden by its mother. It's a good thing placentalism came along, or we'd all have to go through something like this.
Echidna mating is mysterious and primordial. It is also rarely observed, but the following seem to be the basics. It begins when the female goes into estrus. Males, usually three or four of them, but sometimes as many as eleven, start following her around in a long single-file line called an "echidna train" (or even "echidna love train"). It seems very civilized, though it can go on for as long as six weeks, during which time the otherwise solitary animals eat and sleep in each other's company, and the males nip the female's tail, which seems to be a kind of foreplay. Eventually the female echidna climbs partway up a tree, or buries part of herself in the dirt, leaving the males to walk around and around her until they have created a circular rut in the ground. (Sometimes there's only one male, in which case, nothing daunted, he kind of walks back and forth by himself until he has created a little ditch.) Then they engage in a shoving contest. The males that get shoved out of the ditch acknowledge defeat and leave peacefully until only one, the best shover, is left. He gets to mate with the female -- very carefully, because they are both covered with spines. (Understandably, echidnas do it face to face, so don't listen to anyone who tells you that this is a uniquely human behavior.) The male's four-headed penis, which he does not use to urinate, emerges only during the act of mating; the rest of the time he is indistinguishable from a female echidna, as his testicles are also inside his body.
Basically what I'm trying to say is HOLY CRAP MONOTREMES ARE WEIRD WHY DO THEY EVEN EXIST. Also that I really admire them, these life-forms that seem to be built out of spare parts, that refuse to be daunted by the convoluted systems they must use to propagate themselves, that seem as if by rights they really ought to have died out millions of years ago but haven't. Life just won't give up! Life has webbed feet, a bill, a pouch that comes and goes, waterproof fur, spines, poisonous ankles -- whatever it takes. And life is a lot more interesting than the book I have to edit right now, but then so is string cheese. I only wish the male lead really were a platypus.