The area of scientific research that deals with the simultaneous optimization of several (possibly conflicting) criteria is named multi-objective optimization. The ability to efficiently filter and extract interesting data out of large datasets is one of the key tasks in modern database systems. This paper provides a general overview of the most common approaches employed to handle the problem in the field of databases, and describes a novel framework named flexible skylines. After analyzing the main differences between single and multi-optimization problems, I will discuss the three main basic approaches used to handle multi-optimization problems: lexicographic approach, top-k queries and skylines. Each methodology will be discussed, analyzing the pros, the range of applicability and the main issues, which motivate the need to introduce the flexible skylines innovative framework. A review of this approach will show its superiority with respect to the basic approaches, as well as the capability to overcome the majority of their drawbacks.