Trophodynamic ecosystem models are more than 30 years old and there is an increasing number of them, with a growing global coverage. Such models are being used to inform policy and management decision making. With this use comes a responsibility to make clear the implications of uncertainty. At the centre of ecosystem models is the food web. Understanding the true sensitivity of model dynamics to the form and parameterisation of these structures is fundamental for constraining uncertainty. Two decades of experience with such models indicates that parametric sensitivity differs from ecosystem to ecosystem, but structural sensitivity is a universal reality. The coming challenge for trophodynamic models is to remain robust to all forms of uncertainty while remaining flexible enough to capture large scale system shifts and biodiversity turn over under global change.