I first used the term hybrid methods in 1989 to mean a solution technique that combined a direct solver with an iterative technique to solve sparse linear systems. I view this as a way of extending the use of direct methods to larger problems and will argue how this differs from the iterative concept of preconditioning.
I will then talk a little about some recent work in Toulouse on rehabilitating the block Cimmino method, an archetypical hybrid method.