The onset of addiction is marked with drug induced positive experiences that keep being repeated. During that time, adaptation occurs and addiction is stabilized. Interruption of those processes induces polysymptomatic withdrawal syndromes. Abstinence is accompanied by risks of relapse. These features of addiction suggest adaptive brain dynamics with common pathways in complex neuronal networks. Addiction research has used animal models, where some of those phenomena could be reproduced, to find correlates of addictive behavior. The major thrust of those approaches has been on the involvement of genes and proteins. Recently, an enormous amount of data has been obtained by high throughput technologies in these fields. Therefore, (Computational) "Systems Biology" had to be implemented as a new approach in molecular biology and biochemistry. Conceptually, Systems Biology can be understood as a field of theoretical biology that tries to identify patterns in complex data sets and that reconstructs the cell and cellular networks as complex dynamic, self-organizing systems. This approach is embedded in systems science as an interdisciplinary effort to understand complex dynamical systems and belongs to the field of theoretical neuroscience (Computational Neuroscience). Systems biology, in a similar way as computational neuroscience is based on applied mathematics, computer-based computation and experimental simulation. In terms of addiction research, building up "computational molecular systems biology of the (addicted) neuron" could provide a better molecular biological understanding of addiction on the cellular and network level. Some key issues are addressed in this article.