We consider the Conditional Value-at-Risk (CoVaR), which is a risk measure proposed by Adrian and Brunnermeier (2016) to quantify a financial institution's contribution to systemic risk and/or its contribution to the risk of other financial institutions. We discuss two alternative definitions of CoVaR and present its calculations under various dependence structures. Moreover, we discuss possible multivariate generalizations of CoVaR and show their possible use in environmental science.