Simple network models that focus only on graph topology or, at best, basic interactions are often insufficient to capture all the aspects of a dynamic complex system. In this thesis, I explore those limitations, and some concrete methods of resolving them. I argue that, in order to succeed at interpreting and influencing complex systems, we need to take into account  slightly more complex parts, interactions and information flows in our models.This thesis supports that affirmation with five actual examples of applied research. Each study case takes a closer look at the dynamic of the studied problem and complements the network model with techniques from information theory, machine learning, discrete maths and/or ergodic theory. By using these techniques to study the concrete dynamics of each system, we could obtain interesting new information. Concretely, we could get better models of network walks that are used on everyday applications like journal ranking. We could also uncover asymptotic characteristics of an agent-based information propagation model which we think is the basis for things like belief propaga-tion or technology adoption on society. And finally, we could spot associations between antibiotic resistance genes in bacterial populations, a problem which is becoming more serious every day.