Computational models have been of interest in biology for many years and have represented a particular approach to trying to understand biological processes and phenomena from a systems point of view. Much of the early work was rather abstract and high level and probably seemed to many to be of more philosophical than practical value. There have, however, been some advances in the development of more realistic models and the current state of computer science research provides us with new opportunities through both the emergence of models that can model seriously complex systems and also the support that modern software can give to the modelling process. This paper describes a few of the early simple models and then goes on to look at some new ideas in the area with a particular application drawn from the world of mycology. Some general principles relating to how new and emerging computational techniques can help to represent and understand extremely complex models conclude the paper.