Researchers across disciplines apply complexity theory to issues ranging from economic development to earthquake prediction. The breadth of applications speaks to the promise of complexity theory, but there remain a number of challenges to be met, particularly those related to its ontological and epistemological dimensions. We identify a number of key issues by asking three questions. Does complexity theory operate at too general a level to enhance understanding? What are the ontological and epistemological implications of complexity? What are the challenges in modeling complexity? In answering these questions, we argue that, although complexity offers much to the study of place and space, research in these areas has a number of strengths that enhance complexity research.