Science recognizes a number of limitations to its power to predict the future of physical systems. Such limits typically stem from dynamical chaos or the impracticability of dealing with large numbers of variables. In this talk, I will review recent work pertaining to the limits of predictability in complex systems, and to novel features arising in systems involving adaptive agents, such as humans. The ”socio-physics” approach often elicits the criticism (from social scientists) that it ignores the ”reflexive” character of social reality – that valid insights into individual human behaviour, or social patterns, may quickly cause people to alter their behaviour, destroying the validity of those insights. I will argue that reflexitivity is a real phenomenon, but that it’s not a fundamental barrier to socio-economic prediction, for two reasons. First, people under observation often become habituated to their environment and exhibit stable behaviour. Second, science is gaining an ability to model the reflexive process itself, by learning to model the process of human thinking. I’ll conclude by reviewing studies in political science which suggest that a key reflexive feedback driving many of the most recent financial crises has been the evolution of ”triangles” of power among government agencies, regulators and special interests, such as the financial industry. Any successful effort to prevent such crises may need to exert control over such feedbacks, and produce a regulatory framework that is in some sense ”lobby proof.”