Lineages arriving on islands may undergo explosive evolutionary radiations owing to the wealth of ecological opportunities. Although studies on insular taxa have improved our understanding of macroevolutionary phenomena, we know little about the macroevolutionary dynamics of continental exchanges. Here we study the evolution of eight Carnivora families that have migrated across the Northern Hemisphere to investigate if continental invasions also result in explosive diversification dynamics. We used a Bayesian approach to estimate speciation and extinction rates from a substantial dataset of fossil occurrences while accounting for the incompleteness of the fossil record. Our analyses revealed a strongly asymmetrical pattern in which North American lineages invading Eurasia underwent explosive radiations, whereas lineages invading North America maintained uniform diversification dynamics. These invasions into Eurasia were characterized by high rates of speciation and extinction. The radiation of the arriving lineages in Eurasia coincide with the decline of established lineages or phases of climate change, suggesting differences in the ecological settings between the continents may be responsible for the disparity in diversification dynamics. These results reveal long-term outcomes of biological invasions and show that the importance of explosive radiations in shaping diversity extends beyond insular systems and have significant impact at continental scales.