Optimization problems of enormous size and complexity arise in areas from genome sequencing to VLSI design. In this talk we discuss the challenges in working with large-scale models by considering the well-known traveling salesman problem, or TSP for short, which asks for the cheapest way to visit a collection of cities and return to the starting point. For over fifty years the study of the TSP has led to improved solution methods for a wide range of practical problems. We will discuss the history and applications of the TSP and the methods used to attack very large instances. Along the way, we discuss the interplay of modern applied mathematics and increasingly more powerful computing platforms, including computational grids and distributed web-computing.