Optimal Portfolio Theory, as developed during the last twenty‐seven years, represents an important application of mathematics to a very useful field and as such should find its proper place in the education of mathematicians, economists, actuaries, business managers, scientists and engineers. The present article gives a tutorial introduction to Markowitz's basic idea of mean‐variance efficient portfolios and his critical‐line method for obtaining them. A new and simpler approach to implementation of critical line method is given. Some ideas from Pareto optimization are used to get a better insight into the theory. Implication of Maximum Expected Utility and other possible criteria are discussed. The last section gives a list of open problems in the field.