Abstract: The Southern Ocean is home to well known animals such as penguins, seals and whales. It is also a remote and hostile environment and, consequently, understanding of the behaviour and dynamics of these animal populations is uncertain. There are good reasons to develop mathematical models of this ecosystem. Firstly, there is strong evidence for rapid climate change, particularly warming, in parts of the Southern Ocean. This could potentially affect the whole ecosystem, changing the abundance and distribution of the microscopic plants at the base of the food-chain, the small creatures that feed directly upon them, and the fish, birds and mammals feed on these creatures. Secondly, the area has been perturbed by past over-harvesting of whales but still supports important fisheries. It is important to identify ways of managing the fishery which do not increase the negative effects of climate change, prevent the recovery of whales or cause long-term damage to the ecosystem. Modellers have used a variety of approaches to assess how the perturbations of climate change and harvesting might affect the dynamics of the system; to describe the network of interactions between the different species; to identify the species that have the strongest influence on system dynamics; and to assess the risks of candidate fisheries management strategies. One of the key issues is the uncertainty in parameter values, functional relationships and eventual model predictions. Here I give an overview of some of this modelling work, and highlight how explicit assessment of uncertainty helps to clarify the risks associated with fishing and climate change.