Floods and heavy precipitation have disruptive impacts worldwide, but their historical variability remains only partially understood at the global scale. This article aims at reducing this knowledge gap by jointly analyzing seasonal maxima of streamflow and precipitation at more than 3,000 stations over a 100-year period. The analysis is based on Hidden Climate Indices (HCIs). Like standard climate indices (e.g., Nino 3.4, NAO), HCIs are used as covariates explaining the temporal variability of data, but unlike them, HCIs are estimated from the data. In this work, a distinction is made between common HCIs, that affect both heavy precipitation and floods, and specific HCIs, that exclusively affect one or the other. Overall, HCIs do not show noticeable autocorrelation, but some are affected by noticeable trends. In particular, strong and wide-ranging trends are identified in precipitation-specific HCIs, while trends affecting flood-specific HCIs are weaker and have more localized effects. A probabilistic model is then derived to link HCIs and large-scale atmospheric variables (pressure, wind, temperature) and to reconstruct HCIs since 1836 using the 20CRv3 reanalysis. In turn this allows estimating the probability of occurrence of floods and heavy precipitation at the global scale. This 180-year reconstruction highlights flood hot-spots and hot-moments in the distant past, well before the establishment of perennial monitoring networks. The approach presented in this study is generic and paves the way for an improved characterization of historical variability by making a better use of long but highly irregular station data sets.