A procedure is outlined for distinguishing among competing hypotheses for fossil morphology and then used to evaluate current views on the meaning of Neandertal skeletal morphology. Three explanations have dominated debates about the meaning of Neandertal cranial features: climatic adaptation, anterior dental loading, and genetic drift. Neither climatic adaptation nor anterior dental loading are well supported, but genetic drift is consistent with the available evidence. Climatic adaptation and activity patterns are the most discussed explanations for Neandertal postcranial features. Robust empirical relationships between climate and body form in extant humans and other endotherms currently make climatic adaptation the most plausible explanation for the wide bodies and relatively short limbs of Neandertals, and many additional postcranial features are likely secondary consequences of these overall skeletal proportions. Activity patterns may explain certain Neandertal postcranial features, but unlike the situation for climate, relationships in extant humans between morphology and activities are typically not well established. For both the cranium and the postcranium, changes in diet or activity patterns may underlie why Neandertals and Pleistocene modern humans tend to be more robust than Holocene humans.