In this paper, we survey ideas and principles of modeling the investment decision process of economic agents. We start with the criteria of Markowitz of formulating return and risk as mean and variance, and also its extensions. We then look into other related criteria which are based on probability assumptions on future prices of securities. We also present methodologies which, instead of assuming probability distributions, rely on the best solution for the worst case scenario or in the average. A few multiple stage optimization models are discussed. Finally we give a few remarks on some interesting topics for further investigations.