Multi-parametric programming is a mathematical theory to address optimisation problems involving varying parameters. Based on sensitivity and singularity theories, multi-parametric programming derives the optimum solution of the optimisation variables as analytical continuous functions of the varying parameters. In this thesis, novel theory .and algorithmic developments are presented for the solution of various classes of multi-parametric programs with relevance to real-life applications. In Part 1, Advances in global optimisation, particular focus is given to the following classes of global optimisation problems in the context of mUlti-parametric programming: (i) bilevel programming, (ii) multi-level hierarchical and decentralised programming and (iii) multi-parametric mixed integer linear programming. In Part 2, Advances in robust optimisation & control, the foundations towards a comprehensive general theory for robust optimal control are described in detail. These involve two steps, the effective solution of (iv) constrained dynamic programming, and the (v) robust reformulation of the original model-based predictive control problem.