Boilers generate steam continuously and on a large scale. Controlling the boiler process is extremely difficult - it is a highly nonlinear process, its dynamics vary with load and it is strongly multivariable. It is also inherently unstable due to the integrator effect of the drum. In addition, boilers are commonly used in situations where the load can change suddenly and without prior warning. Traditionally, boilers have been controlled by Single-Input, Single-Output (SISO) Proportional plus Integral (PI) controllers. This strategy does not take into account the interaction of the controlled variables or the effect of load on boiler dynamics. This work investigates whether boiler control can be improved by applying multivariable or nonlinear predictive control strategies. Predictive control is a model-based control strategy which is chosen for its ability to handle nonlinear, constrained and multivariable systems. Two nonlinear controllers are developed - a fuzzified linear predictive controller which is based upon several linearised models of the plant and and a nonlinear predictive controller, based upon a single nonlinear plant model. These controllers are compared both with each other and with the conventional PI control strategy. A detailed first-principles model of the boiler is developed for this work. This is used to simulate a boiler plant for controller testing. It is also used to derive a linear state-space model for the linear predictive controller. The nonlinear predictive controllers uses a neural network model.