Mammals make a natural group which subdivides into three, based on their methods of reproduction: the monotremes, the marsupials and the placentals.
All mammals are warm-blooded, they all have at least a few modified hairs, and they generally care for their young. They are usually classified by their teeth.
For each mammal, it is possible to write a dental formula, describing the numbers of each of the different types of teeth in each jaw.
Teeth last long after an animal dies. While teeth are useful in identifying the groups that extinct mammals belong to, there are a few inconsistencies.
According to the dental formula of a koala, it is some sort of fat possum. The molecular evidence, on the other hand, suggests that it is an arboreal wombat.
All of the mammals other than monotremes are viviparous, bearing their young alive. Monotremes are the only furry and warm-blooded egg-layers.
Monotremes have many reptilian features, including egg-laying, their gait as they walk, their egg-laying, and their body temperature, which is more variable.
Marsupials have common features: most of the females (but not all) have pouches in which the young are carried, and the reproductive systems are distinctive.
Placental mammals have their young develop within the uterus, getting nourishment from a placenta, which is fetal tissue in contact with the mother's tissues.