Extracting important relations between biological components and semantic events involving genes or proteins from literature has become a focus for the biomedical text mining community. In this paper, we review a subgraph matching-based approach proposed in our previous work for mining relations and events in the biomedical literature. Our subgraph matching algorithm is formally presented, along with a detailed analysis of its complexity. We present three different relation/event extraction tasks in which our approach has been successfully applied. Our approach is of considerable value in extracting highly precise, binary relations when appropriate training data is available.