Multi-objective optimization (MOO) and decision-making (DM) has become an important research area of evolutionary computations in recent years. The researches on multi-objective evolutionary algorithms (MOEA) focus mainly on the Pareto-based comparison and ordering of individuals, fitness assignment and Riching techniques, etc., so that the population can converge and uniformly distribute in the Pareto front. This paper presents an introduction to the history and classification of multi-objective optimization and decision-making techniques, analyzes both the Pareto-based and non-Pareto-based evolutionary algorithms, and,particularly,the five well-known MOEAs. Some problems related to the researches on MOEAs are addressed in details, such as the characteristics of Pareto front, the test suite and performance evaluation of MOEAs, the MOEA convergence analysis, the MOEA parallelization, and the disposal of real world MOO problems.