Abstract Combining morphological and molecular characters through Bayesian total-evidence dating allows inferring the phylogenetic and timescale framework of both extant and fossil taxa, while accounting for the stochasticity and incompleteness of the fossil record. Such an integrative approach is particularly needed when dealing with clades such as sloths (Mammalia: Folivora), for which developmental and biomechanical studies have shown high levels of morphological convergence whereas molecular data can only account for a limited percentage of their total species richness. Here, we propose an alternative hypothesis of sloth evolution that emphasizes the pervasiveness of morphological convergence and the importance of considering the fossil record and an adequate taxon sampling in both phylogenetic and biogeographic inferences. Regardless of different clock models and morphological datasets, the extant sloth Bradypus is consistently recovered as a megatherioid, and Choloepus as a mylodontoid, in agreement with molecular-only analyses. The recently extinct Caribbean sloths (Megalocnoidea) are found to be a monophyletic sister-clade of Megatherioidea, in contrast to previous phylogenetic hypotheses. Our results contradict previous morphological analyses and further support the polyphyly of “Megalonychidae,” whose members were found in five different clades. Regardless of taxon sampling and clock models, the Caribbean colonization of sloths is compatible with the exhumation of islands along Aves Ridge and its geological time frame. Overall, our total-evidence analysis illustrates the difficulty of positioning highly incomplete fossils, although a robust phylogenetic framework was recovered by an a posteriori removal of taxa with high percentages of missing characters. Elimination of these taxa improved topological resolution by reducing polytomies and increasing node support. However, it introduced a systematic and geographic bias because most of these incomplete specimens are from northern South America. This is evident in biogeographic reconstructions, which suggest Patagonia as the area of origin of many clades when taxa are underrepresented, but Amazonia and/or Central and Southern Andes when all taxa are included. More generally, our analyses demonstrate the instability of topology and divergence time estimates when using different morphological datasets and clock models and thus caution against making macroevolutionary inferences when node support is weak or when uncertainties in the fossil record are not considered.