This chapter discusses the design of metaheuristics for multiobjective combinatorial optimization problems as well as the evaluation of performance in such a context. It focuses on four particular methodologies, namely two evolutionary algorithms (non-dominated sorting genetic algorithm II (NSGA-II) and indicator-based evolutionary algorithm (IBEA)) and two population-based local search algorithms (Pareto local search (PLS) and hypervolume-based multiobjective local search (HBMOLS)). The chapter describes the behavior of these solution methods on different biobjective flow shop variants, in particular for different pairs of objectives, including the makespan of the schedule, the maximum tardiness, the sum of the tardinesses or the number of delayed jobs. A set of instances is proposed, and an experimental study of the degree of correlation between the different criteria is conducted.