This article provides a review of research involving least absolute value (LAV) regression. The review is concentrated primarily on research published since the survey article by Dielman (Dielman, T. E. (1984). Least absolute value estimation in regression models: An annotated bibliography. Communications in Statistics – Theory and Methods, 4, 513–541.) and includes articles on LAV estimation as applied to linear and non-linear regression models and in systems of equations. Some topics included are computation of LAV estimates, properties of LAV estimators and inferences in LAV regression. In addition, recent work in some areas related to LAV regression will be discussed.