We propose a complex systems approach to the study of political belief systems, to overcome some of the fragmentation in the current scholarship on ideology. We review relevant work in psychology, sociology, and political science and identify major cleavages in the literature: the spatial vs. non-spatial divide (ideologies as reducible to a spatially organized set of dimensions vs. as complex conceptual structures) and the person-group problem (ideologies as driven by psychological needs of individuals vs. by institutional and power structures of society). We argue that construing ideologies as conceptual networks of cognitive-affective representations embedded in social networks of people may provide a path for bridging these existing gaps and epistemological disputes. Tools from cognitive science and computational social science such as cognitive-affective mapping, connectionist simulations, and agent-based modeling are appropriate methods for a new research program that substantiates our complex systems perspective on ideology.