The trematode liver fluke, Opisthorchis viverrini, is endemic in Thailand, Lao People's Democratic Republic (Lao PDR) and Cambodia. Its life cycle involves humans, dogs and cats as definitive hosts; and snails and fish as intermediate hosts. Humans get infected through the consumption of raw or undercooked fish. A severe infection of O. viverrini can lead to cholangiocarcinoma, a mostly fatal bile duct cancer. Control activities include treatment of humans and domestic pets, health education on food consumption and improved sanitation. Mathematical modelling can help us to understand this multi-host disease system, identify weak points in the transmission cycle and determine the effectiveness of combinations of interventions to provide rational advice for the planning of control activities. Analysis and simulation of a series of mathematical models, ranging from deterministic ordinary differential equations models to stochastic individual-based models, calibrated to data from two islands in the Mekong river in Lao PDR, suggest that (i) mass drug administration is necessary for elimination of O. viverrini to be achieved as quickly as possible; (ii) sustainable education campaigns are as important as mass drug administration; and (iii) it is unlikely that cats and dogs are necessary for transmission to persist.