Papillomaviruses (PVs) have a wide host range, infecting mammals, birds, turtles, and snakes. The recent discovery of PVs in different fish species allows for a more complete reconstruction of the evolutionary history of the viral family. In this study we combine fossil record estimates and molecular dating to analyze evolutionary events that occurred during PV evolution, as well as to estimate speciation and evolutionary rates. We have used four different data sets to explore and correct for potential biases that particular taxa combinations may introduce in phylogenetic inference. When considering the evolution of speciation rates, we show that these are not constant through time, suggesting the occurrence of evolutionary events like adaptive radiations. We identified four periods along the evolutionary timeline of PVs: (i) a slow increase of PV lineages with an old ancestry that goes parallel to the basal diversification of amniotes; (ii) an initial radiation event of PVs infecting fish, birds, turtles and ancestral mammals; (iii) a secondary radiation event of PVs in parallel to the radiation of placental mammals, that generated a large number of viral lineages; and (iv) a final virus-host co-divergence in parallel to the diversification of PVs within their hosts. When considering the evolution of substitution rates, we show that there are strikingly different trends when stratifying by PV genus, revealing clade-specific events during the evolution of a highly diverse primate PV lineage: the clinically relevant AlphaPVs. We have further explored the effect of heterogeneous taxa representation and the choice of calibration points on the molecular dating of the PV tree. When simultaneously using all calibration points, similar ancestral node ages and overall rates of evolution were obtained with all databases. On the contrary, in our inferences with each calibration point separately, calibrating with younger nodes tended to render higher substitution rates compared to older nodes, also known as the time-dependent rate phenomenon. We discuss that in our case this behavior may be a function of the available host niches and show that a power-law rate decay model performs well to correct for this phenomenon within PVs. Our results provide new insights into the evolutionary history of PVs, where ecological opportunity seems to be the main driving force for the different radiation and key-innovation events we observe and showcases both the potential and limitations of using host-derived calibrations to infer viral speciation times.