Modelling biological systems would be straightforward if we knew the structure of the model and the parameters governing their dynamics. For the overwhelming majority of biological processes, however, such parameter values are unknown and often impossible to measure directly. This means that we have to estimate or infer these parameters from observed data. Here we argue that it is also important to appreciate the uncertainty inherent in these estimates. We discuss a statistical approach--approximate Bayesian computation (ABC)--which allows us to approximate the posterior distribution over parameters and show how this can add insights into our understanding of the system dynamics. We illustrate the application of this approach and how the resulting posterior distribution can be analyzed in the context of the mitogen-activated protein kinase phosphorylation cascade. Our analysis also highlights the added benefit of using the distribution of parameters rather than point estimates of parameter values when considering the notion of sloppy models in systems biology.