Linear Programming, established around 1947 as a serious mathematical approach to solve a multitude of problems arising in engineering and business, has experienced a tremendous development. We are still witnessing today significant progress, in particular in the practical performance of LP algorithms. In this lecture I will present a survey of the theory behind linear programming and of the algorithms that are in use today. I will mention application areas and practical axamples of large scale that can nowadays be solved routinely with the algorithmic machinery available.