In this paper, we look at the complexity and related vulnerability characteristics of Smartgrids. Typical characteristics of complex systems, such as self-organization, emergence, chaotic behavior and evolution, are considered with respect to Smartgrids as future energy infrastructures. These characteristics are categorized as inherent, challenge-response, or acquired. This guides the identification of major sources of uncertainty in the infrastructure. Topological and behavioral characteristics of Smartgrids are also explored with the aim of identifying potential vulnerabilities. We additionally discuss the assumptions, limitations and degree of precision of Smartgrids modeling.