Understanding the epidemiology of cholera, when and where it occurs and how it spreads, is key to its prevention and control. Models can help to apprehend cholera outbreaks by providing insight into critical epidemiological processes, and may be used to evaluate alternative intervention strategies or to predict the future course of epidemics. This thesis aims at advancing the evolution of spatially explicit epidemiological models of cholera outbreaks through methodological developments and practical applications. Over 160 years after John Snow first analyzed the spatial pattern of cholera cases in London and identified water as its pathway of contagion, the disease remains a major public health threat in many regions around the globe. It causes an estimated number of 2.86 (1.30 -- 4.00) million cases and 95 000 (21 000 -- 143 000) deaths in 69 endemic countries every year. A set of metapopulation and individual-based, mechanistic and semi-mechanistic epidemiological models has been developed to tackle epidemiological questions at the country, subnational and city scale. The models explicitly take into account the spatial variability of epidemiological processes such as the spread of the disease through hydrological connectivity and human mobility, or the high resolution spatiotemporal clustering of cases. A method to extract large-scale mobility fluxes from mobile phone call records and directly incorporate them into a model has also been established. Different environmental drivers of cholera epidemics have been taken into account. The models have been applied to recent cholera outbreaks in Haiti, Senegal, Chad and the Democratic Republic of the Congo. Results highlight the important part played by human mobility in the spreading of the disease and the influence of rainfall and other climatic variables as drivers of disease dynamics in several settings. applications demonstrate how models can inform epidemiological policy and show the effect of alternative intervention strategies on the course of an epidemic. The evaluation of the preventive allocation of oral cholera vaccine, antibiotics and/or water, sanitation and hygiene interventions within a given radius around reported cases in densely populated areas shows that such interventions are effective and efficient alternatives to mass intervention campaigns. Moreover, an alternative type of oral rehydration solution proves to have a significant effect on the course of a simulated epidemic. This thesis concludes that the explicit treatment of spatial heterogeneity at an appropriate scale is crucial to reproduce real-world dynamics of cholera outbreaks. It highlights how suitable models can address relevant questions about the dynamics of the disease, provide insights into ongoing epidemics, may aid emergency management and complement current epidemiological practice.