This chapter explains the return-risk trade-off portfolio models. We are going to study the four classic portfolio problems: minimization of risk, maximization of return, maximization of a utility function, and maximization of a risk-adjusted return ratio. We are going to focus on return functions in which the functional form is concave and risk measures in which the functional form is convex because these kinds of functions have a global optimum and can be modeled as convex optimization problems. These kinds of models are widely used by students, academics, and practitioners because they are easier to implement, are very flexible, allow to incorporate real features, and are easy to interpret and explain to nonspecialists.