Complex flow structures consisting of branching, multi-scale, hierarchically arranged flow paths can be a beneficial in certain applications by providing lower hydraulic and thermal resistances than conventional flow arrangements. In this study, an experimental approach was used to investigate the hydrodynamic and thermal effects of the complexity, or degree of branching, in microscale complex flow structures. The primary focus of this work was to develop new concepts to advance the current capabilities of complex flow structures through management of complexity. The effects of complexity were determined from experiments performed on a set of microfluidic test sections which were identical except for the complexity of the underlying microchannel configuration. Comparison of the relative hydrodynamic and thermal performance indicates that complexity has a strong effect on both the pressure drop and heat transfer. When the pumping power is taken into account, the results suggest that higher complexity arrangements improve the overall thermal-hydraulic performance. This conclusion was confirmed by the trends observed in the coefficient of performance, a measure of the device thermal efficiency. To address the limitations of conventional fixed-complexity designs, the concept of a variable-complexity flow structure is developed. With a variable-complexity design, the configuration of a branched flow structure can be dynamically controlled to improve performance as operational conditions vary. This concept was successfully demonstrated by developing and testing an active variable-complexity microfluidic device in which pneumatically controlled microvalves were used to create different flow channel configurations. The variable-complexity concept was further refined by developing a microfluidic device with a passive variable-complexity design in which the flow channel configuration changed autonomously based on local temperatures. By using microvalves containing a temperature sensitive polymer, the flow configuration of the device was made thermally adaptive. Experiments were performed to characterize the behavior of the polymer microvalves and the overall device performance. The results showed that the device was capable of tracking changes in external heat sources by adapting and reconfiguring its internal flow structure. The experiments also showed how this variable-complexity design can reduce the pumping power expenditure by automatically directing flow only to areas where it is required. / text