This survey discusses behavioral and experimental macroeconomics, emphasizing a complex systems perspective. The economy consists of boundedly rational heterogeneous agents who do not fully understand their complex environment and use simple decision heuristics. Central to our survey is the question of under which conditions a complex macro-system of interacting agents may or may not coordinate on the rational equilibrium outcome. A general finding is that under positive expectations feedback (strategic complementarity)—where optimistic (pessimistic) expectations can cause a boom (bust)—coordination failures are quite common. The economy is then rather unstable, and persistent aggregate fluctuations arise strongly amplified by coordination on trend-following behavior leading to (almost-)self-fulfilling equilibria. Heterogeneous expectations and heuristics switching models match this observed micro and macro behavior surprisingly well. We also discuss policy implications of this coordination failure on the perfectly rational aggregate outcome and how policy can help to manage the self-organization process of a complex economic system.