The concept of complexity in chemistry has received much interest in the research community. Various measures to assess molecular complexity have been published, ranging from abstract complexity definitions to very specific application-oriented definitions. In this article we focus on molecular complexity in relation to biological activity. Connectivity and feature-based structural descriptors have been evaluated with reference to their potential as complexity measures. Our goal was to discuss the potential of the complexity concept to support the drug discovery process, helping to design suitable lead candidates. The studies have shown that highly active compounds, on average, are more complex than inactive compounds. However, complexity must be balanced with other molecular properties because more complex molecules have a higher probability to exhibit pharmacokinetic problems.