Widespread flooding, such as the events in the winter of 2013/2014 in the UK and early summer 2013 in Cent ral Europe, demonst rate clearly how important it is to understand the characterist ics of floods in which mult iple locat ions experience ext reme river flows. Recent developments in mult ivariate stat ist ical modelling help to place such events in a probabilist ic framework. It is now possible to perform joint probability analysis of events defined in terms of physical variables at hundreds of locat ions simultaneously, over mult iple variables (including river flows, rainfall and sea levels), combined with analysis of temporal dependence to capture the evolut ion of events over a large domain. Crit ical const raints on such data-driven methods are the problems of missing data, especially where records over a network are not all concurrent , the joint analysis of several different physical variables, and the choice of suitable t ime scales when combining informat ion from those variables. This paper presents new developments of a high-dimensional condit ional probability model for ext reme river flow events condit ioned on flow and r ainfall observat ions. These are: a new computat ionally efficient paramet ric approach to account for missing data in the joint analysis of ext remes over a large hydromet ric network; a robust approach for the spat ial interpolation of extreme events throughout a large river network,; generat ion of realist ic est imates of ext remes at ungauged locat ions; and, exploit ing rainfall information rat ionally within the stat ist ical model to help improve efficiency. These methodological advances will be illust rated with data from the UK river network and recent events to show how they cont ribute to a flexible and effective framework for flood risk assessment, with applicat ions in the insurance sector and for nat ional-scale emergency planning.