This talk reviews methods for synthesizing and analyzing controllers for linear parameter varying (LPV) systems. This class of systems was widely studied in the early 90's to formalize the use of ad-hoc gain-scheduling in industry. The talk reviews the existing results for LPV systems and covers recent progress on numerical algorithms for these systems. First, techniques are described to model practical systems within the LPV framework. Next, the existing analysis and controller synthesis conditions are summarized. These conditions lead, in some cases, to parameterized linear matrix inequalities (LMIs). The talk discusses heuristic algorithms to approximately solve these parameterized LMIs. Finally, recent results on robustness analysis for LPV systems using integral quadratic constraints are provided.