This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.