We review major developments in multi-objective optimization over the past decades. Although mathematical foundations and basic concepts have been established earlier, substantial progress in methods for constructing and identifying preferred solutions started in the late 1950s. We classify these approaches into two broad categories: mathematical programming-based and population-based. The former originated in the late 1950s, and its growth accelerated from the 1970s onward. We differentiate between approaches dealing with problems that operate in a continuous solution space and combinatorial problems where some variables are restricted to integer values. Population-based approaches flourished in the 1990s. Our focus is on evolutionary computation techniques that either aim to discover the entire Pareto front or incorporate the decision maker's preferences to select the most favorable solution(s) or bias the search toward preferred regions. For all categories, we discuss those approaches that, in our opinion, have made major impacts. We examine current research trends and speculate on future directions in the field.