Okay, mammalian evolution is based on an extensive amount of theorizing founded on a relatively small amount of evidence. This is not to say it’s necessarily wrong, just that it tends to validate tentative hypotheses on relatively scanty evidence, and then change them, sometimes repeatedly, as new evidence comes to light. (Think of it as like a good detective novel or show, where the preponderance of the evidence points first one way, then another, then a third, as more evidence comes to light.)
For the first 150 million years of mammal existence, the various groups of mammals occupied econiches of small, probably nocturnal, insectivorous (and possibly fructivorous) roles. Anything larger was occupied by archosaurs. These groups are predominantly identified by their teeth, which are the best-preserved remains by and large, and which had characteristic cusp patterns. Among them are the docodonts, the triconodonts, the morganucodonts, the symmetrodonts, etc. Prior to any effort to reflect evolutionary lineages, they were grouped together as Subclass Prototheria, which was then abandoned as they came to be thought of as offshoots along The Road to Placentaldom. Quite recently, other studies have suggested that they do comprise a true clade, and resurrected Prototheria as its name.
The Monotremes almost certainly are surviving Prototheres, probably of a separate group without Mesozoic representation (unless I’m not up to date here) but closely allied to the Docodonts.
Late in the Jurassic, one group evolved to somewhat larger size, and a fruit-and-nut-eating lifestyle, convergent on modern sciuromorph rodents (squirrels, woodchucks, and relatives). These forms survived through the Cretaceous and past the K-T break well into the Eocene. They are the multituberculates (again a tooth-structure-based name) and were the sole members of Subclass Allotheria. What cladistics has done with them, I’m not sure.
Finally, in the Cretaceous, a group called the pantodonts evolved. As of the last I knew, they were considered either the common ancestor, or close relatives of an unknown common ancestor, to the Eutheria, the combined marsuipals and placentals.
To the best of my knowledge, marsupials are still considered a clade, but more and more evidence is mounting up to suggest a very early split into two groups, each of which split into two large secondary groups. Based on where most of their surviving members are found, the two main groups are the Australodelphia and the Ameridelphia. Both groups diverged widely and produced forms convergent with a wide assortment of placentals. Following the Great American Interchange at the end of the Tertiary, most of the larger forms among the Ameridelphids died off – the borhyaenids, thylacosmilids (marsupial sabertooth), etc. While I have not yet seen this, I would be totally unsurprised to see a theorist splitting the marsupials into two independently evolved clades.
The placentals definitely conmprise a clade – the common derived features shared by all placentals and absent from everything else including marsupials argue strongly for this. Within the placentals, however, the classic 22 orders have been largely tossed on the scrap-heap, and here is an enormous amount of DNA- and mt-DNA and new-fossil based theorizing about relationships. The one point that seems to have gained consensus is that the Xenarthra (AKA the Edentata: anteaters, sloths, and armadillos and their extinct allies) constitute a sister group to a clade of all other placentals. There is a scad of anatomical and genetic evidence pointing to this. Slightly-out-of-date accounts will throw the Philidota, the pangolins (“scaly anteaters”) in with them, but contemporary thought says otherwise.
Within the non-edentate placentals, there is a ferment of hypotheses about relationships, based in part on new fossil finds but even more on genetic markers shared by living forms. For example, the closest relatives of the Artiodactyls – the “even-toed ungulates”: pigs, hippos, camels and llamas, deer, antelopes, sheep, goats, cattle, and all their sisters and their cousins and their aunts – seem to have been the extinct Mesonychids, large hoofed carnivores of the earliest Cenozoic, and the whales and dolphins. The relationships are so close, in fact, despite external appearances, that a Clade Cetioartiodactyla has been created, the point being that a pig apparently is as closely related to a whale or dolphin as it is to a camel or yak.
Closest relatives to the primates (man, apes, monkeys tarsier, lemurs, and allies) seem to be the tree shrews and the colugos (“flying lemurs”, a name that like the Holy Roman Empire seems to have stuck despite failing on multiple groups). The term Scandentia is sometimes applied to the broad group and sometimes to the tree shrews exclusively. Depending on your theorist of choice, next closest would be either the bats or the rodents – unless someone has advanced a new theory.
I imagine that Colibri or Darwin’s Finch may have some more detailed (and possibly more up-to-date) comments on the placental-order shuffle. But I wanted to paint the broader picture to the extent I know it.