I inferred time-calibrated phylogenies for the tropical plant genus Ipomoea, and used this a a framework to address theoretical questions about the kinds of information about evolution that can be derived from a phylogeny constructed from genomic sequence data. I focused particularly on understanding temporal patterns of evolutionary diversification, and showed that there are fundamental limitations to the precision with which inferences can be made - even when analysing genomic scale datasets. These limitations have been overlooked in previous studies, resulting in inferences that are misleadingly precise. Nonetheless, I showed that when specific hypotheses are addressed, novel insights can be derived from time calibrated phylogenies. In the context of Ipomoea we showed that the sweet potato (Ipomoea batatas) evolved in pre-human times, and that there are marked increases in speciation rates in specific clades within Ipomoea that are of a scale equivalent to some of the most iconic radiations in the plant kingdom.