The roots of complexity research and theory can be found in general and dynamic systems theories, chaos theory, information theory, and cybernetics. Complexity acknowledges the fact that everything is organized with a complex network of patterns and connections, and that everything exists within an "uncertain state between order and disorder" (Dean, in Vitek & Jackson, 2008, p. 82). The study of complex systems looks for the patterns and behavior that emerge from systems; in other words it is a study of the emergence of the collective behavior of a complex network, where the result is more than a simple sum of the parts of the system. Complexity looks to the interactions between parts of a system as well as the parts itself for insights into how networks and complex systems function.

Qualitative research that seeks to identify patterns or studies specifically the relationships and processes between individuals or actions can be informed by complexity theory. Inquiry based on grounded theory work, for example, could benefit from asking systems thinking and complexity research-based questions. While grounded theory generally looks for causal relationships, application of complexity theory may add multiple dimensions to the causes, or in fact show that behavior can emerge from an unidentifiable or unpredictable combination of causes.

According to the New England Complex Systems Institute, “there are three interrelated approaches to the modern study of complex systems, (1) how interactions give rise to patterns of behavior, (2) understanding the ways of describing complex systems, and (3) the process of formation of complex systems through pattern formation and evolution” (http://www.necsi.edu/guide/study.html). The study of complex systems has applications in nearly every field, from mathematics to psychology to neurobiology to economics. The application of systems thinking in any qualitative inquiry can help the researcher consider her problem in multiple dimensions or directions, and includes paying special attention to all feedback loops in the process. It can help dig deeper, seeing past initial cause-and-effect discoveries into the real root of an issue or cause of a problem. It may also help keep researchers cognizant of the fact that their good actions in one part of a system may in fact have unintended consequences in another part of the system.

The study of complex system helps inform other areas of research such as web science, systems dynamics, autopoiesis, and self-organization. It allows researchers to break away from prior models that relied primarily on linear thinking. Complexity is based in non-linearity, and while the research may study cause and effect it is as a significant departure from a linear view. In other words, something that pushes in the system here may have an effect in a completely unexpected part of the web, rather than directly inline with the point of disturbance.

A wide variety of inquiry methods can be informed by basic concepts used in the study of complexity. For example, in studying complex systems multi-scale descriptions are important. In other words, large- and fine-scale descriptions, and how they relate to one another, are important to collect. For example, atoms, molecules, cells, organs in the body. Researchers must also be aware that some fine-scale actions will influence larger systems, for example the butterfly effect in weather (see Bar-Yam, 2007, http://www.necsi.edu/guide/points.html).

Codynamics is the practical application of complexity science to the management of organizations.

Network science is the study of the interrelationships within and among networks of any type. Network science has a range of subfields, from meta-network analysis to small-world to scale-free networks.

Studies in feedback effects are also related to complexity research. Fractal science is a good example of this, where geometric forms are generated through recursive feedback mechanisms.

Berkes, Colding, and Folke in Navigating Social-Ecological Systems: Building Resilience for Complexity and Change (2003) apply a fully realized complexity model, including adaptive feedback loops, resiliency, and the multiprocess loop of panarchy complexity modeling, to several case studies in local management systems, learning and adaptation, and across scales of management systems.

Another example of complexity research is Lansing's research on Balinese subak irrigation systems and how irrigation, worship, and rice cultivation networks represent a complex adaptive system demonstrating a co-evolution of cultural diversity, worship, persevering economies, and sustainable farming and cultural practices over a thousand year period. Many of the interweaving complex factors were almost invisible to outside researchers and the complexity far outpaced researchers' computer models.