Much decision making in industry is based on rules-of-thumb, which are either validated via mathematical modelling or simulations. The Mathematics-in-Industry Study Group meetings, organized by Australian and New Zealand Industrial and Applied Mathematics, have played an important role in fostering stronger contacts between mathematicians and statisticians and industrial partners. The speakers will discuss some representative examples where the resulting solutions have had considerable subsequent impact. Even in industrial modelling and simulation, a key issue is the management of uncertainty, so that useful rules-of-thumb are identified even though the models on which they are based are only approximations of the reality of the processes being investigated. The management of uncertainty in industrial modelling and simulation is often achieved by identifying an appropriate simple model that encapsulates the answer to the question under consideration. Various examples will be discussed.