The pioneering work of Harry Markowitz on classical portfolio optimization is the base of this paper. Markowitz tried to generate efficient portfolios with only two statistical numbers maximize portfolio return while minimizing the risk of the portfolio. Although his theory has assumed a firm position in science, in practice it often reaches its limits. Markowitz used values from past to estimate future returns, variances and correlations. In reality, the price performance of a security is different from its past values. And to select an optimal portfolio on just two variables you either need normally distributed stock prices or a quadratic utility function for the investor. Both conditions are not fulfilled in practice. Empirically it can easily be observed that security prices are not normally distributed and also the individual preferences of an investor cant be clearly represented in a quadratic utility function.Therefore, the classical portfolio optimization of Markowitz should be treated with care. Because of these weaknesses a number of new, alternative investment theories have evolved over time, which should lead to more stable solutions. Some of these alternative approaches, beyond the classical portfolio theory, are presented below.