This paper studied the dynamics of civilian and military fatalities in the Iraq War during the 2003-2010 period. R/S-scaling analysis, a method to characterize fractality and memory effects in sequences, was used to estimate time variations in the correlations of daily fatalities. Together with concepts from complex social networks and systems theories, the dynamics of correlations (measured in terms of the so-called scaling Hurst exponent) provide a framework to describe the Iraq War evolution and to evaluate the effects of the major military and political events. In terms of changes in a correlations parameter, five regimes in the evolution of the war were identified. The first regime, occurring in the first months after the invasion, corresponds to a conventional confrontation. In the second regime occurred in the last months of 2004, the dynamics of civilian fatalities evolved toward uncorrelated behavior, indicating that the occurrence of daily fatalities was basically governed by random processes. This is in contrast to the dynamics of military fatalities that showed increased correlations. The second regime can be seen as the advent of a chaotic episode where the different insurgency groups acted within an erratic, poorly coordinated, manner. In the third regime that occurred in the first two 2005 quarters, correlations of civilian fatalities increased and converged into the correlations patterns of military fatalities, and this was interpreted as the surging of a well-organized, although non-centralized, insurgency structure. The fourth regime lasted from mid-2005 to the last 2007 months and showed an important correlation decrement for the military fatalities. This was related to the clash of two antagonist war structures, namely, the traditional centralized Coalition Army and a non-centralized insurgent army. Finally, the fifth regime, from mid-2007 to date, is characterized by stable fatality dynamics converging to uncorrelated behavior. It is apparent that this behavior is related to the start of the endgame to achieve stable economy and government. The concept of a scale-free network was used to describe the insurgency operations and the subsequent war and political events oriented to incorporate the former Baath Party member in the formation of a national Iraqi government. It is concluded that, given the availability of data (fatalities, economic activity, migration, etc.) in contemporary conflicts, the usage of mathematical methods and tools would provide further insights of the conflict evolution and, in this way, help to design better policies and strategies to reduce the adverse effects of violence on civilians.