System complexity is a challenge both with regard to defining and agreeing on basic concepts of system dependability, and to actually achieving such dependability in practice from large computer-based systems. In this talk I will discuss such issues, and give a brief description of some recent work on a new approach to formally modelling and analysing the activity of complex (un)dependable systems. I will end by discussing some likely dependability and security consequences of the overall complexity and chosen architecture of the huge National Programme for IT (NPfIT) that is currently being undertaken by the National Health System in England, and which is claimed to be the world's largest civil IT project.