The Euclidean Steiner tree problem is the problem of constructing a shortest
possible network interconnecting a set of given points in the Euclidean plane.
The history of this problem goes back to Gergonne in the early 19th century.
Applications of the problem have been from designing canal networks to the
layout of wiring on VLSI chips and more recently to the design of the layout of
the network of tunnels in an underground mine. In this talk I will describe work
across two centuries inspired by the fascinating Steiner tree problem.