The mean-variance model has been very successful among academics and students; however, it has not been widely adopted by practitioners in the asset management industry because it mainly suffers from two problems: the lack of robustness and the lack of diversification. The lack of robustness means that the optimal portfolio weights are highly sensitive to small changes in the expected return vector and covariance matrix because it maximizes the estimation errors of input parameters. The lack of diversification means that the mean-variance model generates portfolios with extreme weights or concentrated on few assets. These two problems apply in general to return-risk trade-off portfolios because classic objective functions tend to produce corner solutions that are less diversified and highly sensitive to input parameters. In this chapter we explain some approaches that help us to overcome these problems.