This HDR manuscript provides an overview of my scientific activity which revolves around the development of probabilistic models enabling the production of uncertain hydrologic predictions. This activity stretches from applied statistics to hydrology, but with a clear asymmetry: the former provides the toolbox while the latter is the objective. The manuscript is divided in three chapters: Chapter 1 "Uncertainty in streamflow data" focuses on the production of streamflow time series, and in particular on the uncertainties affecting the rating curve used for this purpose. It describes the development of the generic BaRatin method (Bayesian Rating curve), along with other tools addressing hydrometric challenges such as rating shifts or complex rating curves for stations influenced by e.g. vegetation or backwater effects. Chapter 2 "Uncertainty in and around Hydrologic Models" turns the focus to hydrologic models, and in particular the input, response and structural uncertainties that affect them. It revolves around the development of the BATEA framework (Bayesian Total Error Analysis) to decompose the total predictive uncertainty into its constitutive sources, and the many challenges that accompanied this development. Chapter 3 "Hydrologic variability" describes the development of probabilistic models of increasing flexibility to describe hydrologic variables. These models may vary in time, vary conditionally on some predictor, vary in space, be multi-variable or a combination of these properties. An underlying motivation behind these developments is to make the best possible use of available data to better understand the natural hydro-climatic variability, with a particular focus on extremes.