A recent focus of computational biology has been to integrate the complementary information available in molecular profiles as well as in multiple network databases in order to identify connected regions that show significant changes under different conditions. This allows for capturing dynamic and condition-specific mechanisms of the underlying phenomena and disease stages. Here we review 22 such integrative approaches for active module identification published over the last decade. This article only focuses on tools that are currently available for use and are well-maintained. We compare these methods focusing on their primary features, integrative abilities, network structures, mathematical models, and implementations. We also provide real-world scenarios in which these methods have been successfully applied, as well as highlight outstanding challenges in the field that remain to be addressed. The main objective of this review is to help potential users and researchers to choose the best method that is suitable for their data and analysis purpose.