In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason about a variety of topic areas in linear algebra, as well as studies that provide evidence of promising directions for supporting students' success through various teaching interventions and experiments in the classroom. From this survey paper, we identify areas for future research into the teaching and learning of this increasingly important area for modern applications.