In this paper, we provide a brief overview of the field of complexityresearch in economics, and discuss directions of research that weconsider to be promising in terms of solving open issues. We start thesurvey of the field with the research that emerged in the 1990s, whenunder the influence of earlier developments in the natural sciences(e.g., thermodynamics and chaos theory), the term complexity became infashion to refer to theoretical ideas about how "ordered" patterns at anaggregate level can emerge from interaction between heterogenous agentsat the microeconomic level. This gave rise to the notion ofself-organization in dissipative systems, or "order at the edge ofchaos" to describe economic dynamics. Because disequilibrium plays alarg...