Research on extracting biomedical relations has received growing attention recently, with numerous biological and clinical applications including those in pharmacogenomics, clinical trial screening and adverse drug reaction detection. The ability to accurately capture both semantic and syntactic structures in text expressing these relations becomes increasingly critical to enable deep understanding of scientific papers and clinical narratives. Shared task challenges have been organized by both bioinformatics and clinical informatics communities to assess and advance the state-of-the-art research. Significant progress has been made in algorithm development and resource construction. In particular, graph-based approaches bridge semantics and syntax, often achieving the best performance in shared tasks. However, a number of problems at the frontiers of biomedical relation extraction continue to pose interesting challenges and present opportunities for great improvement and fruitful research. In this article, we place biomedical relation extraction against the backdrop of its versatile applications, present a gentle introduction to its general pipeline and shared resources, review the current state-of-the-art in methodology advancement, discuss limitations and point out several promising future directions.