Didelphid marsupials (a New World clade in which embryos are born into a second womb before graduating to a pouch) were present in North America from the start of the Cenozoic.  They spread to South America in the Paleocene (where they evolved along the same lines as Arel's opossums) and to Asia in the Eocene (but later went extinct).  Most of these creatures are arboreal insectivores(bottom left), but some predators, such as the nocturnal possum-houns (top) and drop-bears (bottom right) evolved during the ecological turmoils of the Pleistocene and have managed to hold onto their niches despite competition from dinosaurian predators.  These carnivorous forms live in both North and South America, but are at their largest in North America's boreal forests.

Bats evolved during the Eocene from a primate/rodent complex (the rodents have since died out---eaten by a pack of armadilloes, most likely) and are almost exactly the same as they are in Arel.

Like Brian says:  herbivorous diprotodont dentition has evolved while jackal-sized predators successfully compete with small theropods - although they have not produced anything bigger than 12 kg.

As in RL, monotremes are only around in Australia, and these are the semi-aquatic platipi (Brian doesn't like echidnas for some reason---best not to ask)

Methatheres are a group of ancient mammals, possibly related to the monotremes (and if so, only very distantly).  They lactate and bear their young live, but they are not viviparous, but oviviparous, hatching their eggs internally, rather going through a true, eutherian pregnancy.  This group probably evolved in Asia some time during the Mesozoic (Jurassic?), and occupied a number of weasle-like forms during the most of the Tertiary.  Now, with doglike kochillas and catlike felimuses competing for space, most metatherians are semi-aquatic.  A few very large forms (such as the each-uiges) have evolved, and some are marine.  Metatherians may be found in Eurasia and Africa (where they are smaller),  but not in the New World.

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