A motivating introduction to Semi-Infinite Programming (SIP) is presented, including a sample of its many applications to different subjects like pollution control models, functional approximation, pattern recognition, geometric and semi-definite programming, Neyman-Pearson theory, etc. In the particular setting of linear SIP, some basical results related to optimality and duality theory, as well as some stability results are reviewed, emphasizing the main differences with the ordinary linear programming problem.