Regression testing research has received significant focus during the past decades, acknowledging the benefits it can provide to organisations in terms of reduced development and maintenance costs, as well as sustained end-user satisfaction. There are several challenges left to overcome before the industry can fully take advantage of the available research results in this area. To get a better overview of how current regression testing research fits in with todays industrial practices, we read a selection of papers in the field and based on our experience, critically examined their content. As a result, we present and discuss a taxonomy of regression testing challenges, from the perspectives of both methods and organisations, that we believe will foster the industrial uptake of regression testing.