Around the late 90s, CVaR minimization (Rockafellar and Uryasev, 2000) and nu-SVM formulations (Schoelkopf et al., 2000) were introduced simultaneously and independently in different literatures: financial risk management and machine learning. In this talk, we provide an introduction to a series of our papers about interactions between CVaR minimization problems and nu-SVMs. First, we introduce a CVaR-based linear discriminant model (Gotoh and Takeda, 2005) and its equivalence to the Enu-SVM (Perez-Crus et al., 2003). Secondly, we provide referral to CVaR minimization models which are supported by a theory for the nu-SVMs. A relation to robust optimization and recent results will also be mentioned.