In this lecture I will survey - aimed at a broad mathematical audience - the development of linear and integer programming. The history of these subjects began about one and a half centuries ago but their “boom” started in the 1950s only. Theory, algorithm design and analysis dominated the first years of development. Computational progress was particularly significant in the last twenty years. In fact, the advances in linear and integer programming software are on at least the same level as those in computing machinery.

These achievements combined with successful efforts to model applications make it possible to solve today real world problems of breath taking size and diversity. I will report about some of these success stories in my talk.