This working paper addresses the question posed in the title via a survey of 20 or so experienced healthcare modellers and a literature review of over 100 books and articles. Four levels of 'genericity' are proposed: generic principle model, generic framework, setting-specific generic model and setting-specific model. The third and fourth of these are then chosen as the focus for a further in-depth examination to extract lessons relevant to the problem of building a 'whole-hospital' model for emergency patients. Many examples of models of individual hospital departments are found and a much smaller number of multi-department models. Many of these do not report validation or implementation processes. Nevertheless potentially valuable lessons can be learned.