Hemiptera, the fifth most diverse insect order, are characterized by their high diversity in deep time, with 145 known extinct families. However, the precise timing of the origin of Hemiptera lineages has remained uncertain. Traditional approaches, molecular clock analyses and fossil calibrations, have overlooked much of this extinct diversity by failing to incorporate key fossil data. Furthermore, no estimates have been proposed for the timing of the extinction of Hemiptera's fossil lineages. In this study, we use the recently developed Bayesian Brownian Bridge model, which estimates the timing of lineage origin and extinction through fossil-based Bayesian modelling, to provide a temporal framework for the rise and fall of 310 major hemipteran lineages. Our results support an early Pennsylvanian origin of Hemiptera, and indicate that the major hemipteran lineages originated between the late Carboniferous and Late Permian (Pennsylvanian-Lopingian). Additionally, our analyses reveal a radiation of Hemiptera during the Permian (Guadalupian), followed by multiple extinctions of ancient hemipteran lineages from the Permo-Triassic boundary to the mid-Triassic. A second major radiation occurred during the Cretaceous, coinciding with numerous extinctions of relic and newly emerging Cretaceous lineages, highlighting a faunal turnover. Our study provides a holistic fossil-based picture of the evolutionary history of Hemiptera.