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The recent Generalised Predictive Control algorithm (Clarke et al, 1984,87) is a self-tuning/ adaptive control algorithm that is based upon long-range prediction, and is thus claimed to be particularly suitable for process control application. The complicated nature of GPC prevents the application of standard analytical techniques. Therefore an alternative technique is developed where an equivalent closed loop expression is repeatedly calculated for various control scenarios. The properties of GPC are investigated and, in particular, it is shown that 'default' values for GPC's design parameters give a mean-level type of control law that can reasonably be expected to provide robust control for a wide variety of processes. Two successful industrial applications of GPC are then reported. The first series of trials involve the SISO control of soap moisture for a full-scale drying process. After a brief period of PRBS assisted self-tuning default GPC control performance is shown to be significantly better than the existing manual control, despite the presence of a large time-delay, poor measurements and severe production restrictions. The second application concerns the MIMO inner loop control of a spray drying tower using two types of GPC controller: full multivariable MGPC, and multi-loop DGPC. Again after only a brief period of PRBS assisted self-tuning both provide dramatically superior control compared to the existing multi-loop gain-scheduled PID control scheme. In particular the use of MGPC successfully avoids any requirement for a priori knowledge of the process time-delay structure or input-output pairing. The decoupling performance of MGPC is improved by scaling and that of DGPC by the use of feed-forward. The practical effectiveness of GPC's design parameters (e.g. P, T and λ) is also demonstrated. On the estimation side of adaptive control the current state-of-the-art algorithms are reviewed and shown to suffer from problems such as 'blowup', parameter drift and sensitivity to unmeasurable load disturbances. To overcome these problems two novel estimation algorithms (CLS and DLS) are developed that extend the RLS cost-function to include weighting of estimated parameters. The exploitation of the 'fault detection' properties of CLS is proposed as a more realistic estimation philosophy for adaptive control than the 'continuous retention of adaptivity'.