This thesis considers the use of barrier functions in the context of constrained model predictive control (MPC). A new class of controller is developed by including a weighted barrier function in the objective that ensures inequality constraints are satisfied. Fixing the barrier weighting term to be some positive value possibly much greater than zero has interesting effects on controller dynamics, particularly near constraint boundaries. When the barrier weighting term is close to zero, the corresponding dynamic behaviour resembles that of standard MPC. In fact standard MPC is subsumed within the new class as a special limiting case; in this way, the new class may be seen as a generalisation of standard MPC. Conditions are determined for the barrier such that correct steadystate behaviour is guaranteed; a barrier satisfying these conditions is called a recentred barrier and consequently the new controller class is called recentred barrier function MPC (abbreviated as r-MPC). The barrier approach shares the same fundamental philosophy as interior-point methods a connection which is exploited throughout this thesis. For example, interior-point geometry is exploited to show nominal closed-loop stability of r- MPC for the case of linear system models. Similarly, algorithms for solving the associated optimisation problem can be developed in a natural manner. Indeed, the algorithms developed in this thesis are modifications of existing interior-point algorithms; they also maintain the polynomial complexity exhibited by the latter. The new controller class is validated via a successful industrial application to edible oil refining. The industrial trials demonstrate how the barrier weighting parameter can be interpreted as another tuning parameter for the controller. Changing the weighting value has the effect of adjusting controller caution near constraint boundaries.