This lecture will present a broad overview of complex macroscopic behaviour arising in many-body systems through the combination of competitive interactions and disorder, even with simple ingredients at the microscopic level. An attempt will be made to indicate and illustrate the richness that has arisen, in conceptual understanding, in methodology and in application, across a large range of scientific disciplines, together with a hint of some of the further opportunities that remain to be tapped. The perspective will be that of physics, trying to show how concepts and methodologies of physics have contributed and been stimulated.