This chapter focuses on nonlinear portfolio construction. We utilize quantile regression to study tail risk and incorporate it into portfolio optimization. Using 1970 to 2019 S&P 500 data, we perform an empirical study constructing realistic stock selection investment strategies. The results indicate that quantile optimization produces practical portfolios with risk levels, diversity, and turnover comparable to the classical mean-variance approach. Moreover, the median portfolio from our study outperforms the mean-variance portfolio consistently over the entire period studied, and the portfolio minimizing the left tail risk outperforms those from other percentiles and the mean-variance approach when the market is moving downward.