The marsupial frogs are found over a great part of South America, being particularly diverse in upland regions. Many (particularly members of the genus Hemiphractus) are somewhat gargoyle-ish beasts with flattened heads and/or prominent 'horns' above the eyes. Until recently, marsupial frogs were usually classified as a subfamily of the treefrog family Hylidae but more recent phylogenetic studies have agreed on the polyphyly of the latter family in its broad sense. As a result, the marsupial frogs are now placed in their own distinct family, the Hemiphractidae, as part of a broader association of a number of South American frog families. The influential phylogenetic study of amphibians by Frost et al. (2006) suggested that the marsupial frogs themselves were polyphyletic and divided them between no less than three families (Hemiphractidae, Cryptobatrachidae and Amphignathodontidae) but more recent studies have agreed on their monophyly. Frost et al.'s results are generally thought to have resulted from their poor coverage of members of this clade.
So what makes them marsupials? In all hemiphractids, the female carries her eggs after fertilisation until they hatch. In three of the five recognised genera (Hemiphractus, Cryptobatrachus and Stefania), the eggs are carried exposed on the surface and the young hatch directly as fully-formed froglets without a free-living tadpole stage. In the other two genera, Flectonotus and Gastrotheca (the latter genus being the most diverse in the family), the eggs are contained in a pair of pouches on the female's back. In some Gastrotheca species the eggs hatch into froglets as in the other genera, but in other Gastrotheca and in Flectonotus they hatch into tadpoles that the female then releases into a suitable pool of water.
Considering that a tadpole stage in development is evidently the original condition for frogs as a whole, it might be assumed the tadpole-bearing hemiphractids represent the basal taxa in the group with loss of the tadpole being derived. But intriguingly, recent phylogenetic analyses have indicated that the tadpole-bearing Gastrotheca occupy quite deeply nested positions in the hemiphractid family tree (Wiens et al. 2007; Flectonotus is placed as the sister taxon of all other hemiphractids, more as one might expect). This has led to the suggestion that the presence of tadpoles in Gastrotheca may represent a reversal to the original condition from direct-developing forebears. Now, I'm going to admit up front that I tend to be skeptical about claims for the reappearance of complex characters (and only partially because such studies never fail to cite that "stick insects re-evolved wings" thing of which I've already said I'm not a fan). In their analysis of breeding trajectories in hemiphractids, Wiens et al. (2007) found that, if one assumed that loss of the tadpole stage was equally likely to its gain, then the hemiphractid phylogeny supported a re-gain of tadpoles. However, if one presumed that loss was more likely than gain, then their analysis supported multiple losses with the tadpole-bearing Gastrotheca retaining the ancestral state. Nevertheless, they argued that a re-gain was more likely. Tadpole-bearing hemiphractids are all inhabitants of high altitudes where their young are often the only tadpoles about, suggesting that competition with other frogs excludes them from lower altitudes. Assuming multiple origins of direct development would require that the low-altitude hemiphractids evolved from low-altitude tadpole-bearers of which there is no current sign. But could it be that more recent changes in the South American environment changed the competitive regime for hemiphractids? Have the frog lineages that supposedly exclude them for lower altitudes been in the area for as long as the hemiphractids have? On the other hand, hemiphractids are unusual among direct-developing frog in that their embryos still develop some tadpole-like features (such as an incipient beak) only to lose them before emerging from the egg. Could this retention of ancestral features in an incipient form made it easier for them to re-establish at a later date?
There is an evolutionary reversal among hemiphractids that seems more unequivocal, however: one species, Gastrotheca guentheri, is the only known frog in the modern fauna to have teeth in the lower jaw (Wiens 2011). There are a number of other frogs (including some other hemiphractids) in which the lower jaw has tooth-like serrations but G. guentheri is the only species with honest-to-goodness teeth. There seems little doubt that this is a true reversal; for G. guentheri to be the only living frog species to retain the ancestral state would require close to two dozen independent losses with no sign of the feature's retention elsewhere. In this case, while other frogs do not have teeth in the lower jaw, many of them do have teeth in the upper jaw (in some, such as Hemiphractus species, these upper teeth may be modified into prominent fangs for prey capture). So the genes for tooth development are still in place; presumably, G. guentheri has been able to re-develop its lower teeth through the genes for upper teeth being effectively re-deployed to take action elsewhere.
Frost, D. R., T. Grant. J. N. Faivovich, R. H. Bain, A. Haas, C. F. B. Haddad, R. O. de Sá, A. Channing, M. Wilkinson, S. C. Donnellan, C. J. Raxworthy, J. A. Campbell, B. L. Blott., P. Moler, R. C. Drewes, R. A. Nussbaum, J. D. Lynch, D. M. Green & W. C. Wheeler. 2005. The amphibian tree of life. Bulletin of the American Museum of Natural History 297: 1–370.
Wiens, J. J. 2011. Re-evolution of lost mandibular teeth in frogs after more than 200 million yeatrs, and re-evaluating Dollo's Law. Evolution 65 (5): 1283–1296.
Wiens, J. J., C. A. Kuczynski, W. E. Duellman & T. W. Reeder. 2007. Loss and re-evolution of complex life cycles in marsupial frogs: does ancestral trait reconstruction mislead? Evolution 61 (8): 1886–1899.