We contrast and evaluate two of the most popular responsible investing strategies employed at present: negative screening and engagement. As a backdrop, we consider the challenges faced by the University of Cambridge, which mirror those experienced by institutional investors worldwide. Specifically, we make use of issues raised at the recent “Divest or Engage?” conference at the University. We discuss emerging academic evidence from recent, and hitherto unpublished, papers in order to provide an up-to-date perspective. We describe the challenges in excluding undesirable assets from investment portfolios and present evidence on the effectiveness of engaging with investee companies. The strategies of divestment and engagement are often employed as complements to each other and this can be advantageous. We caution that investors need to be aware of the disquieting evidence that ESG metrics differ considerably across rating services, and the choice of data provider can have a fundamental impact on the ESG credentials of institutional portfolios.