Harmony search algorithm and its variants have been used in several applications in medicine, telecommunications, computer science, and engineering. This article reviews the global and multi-objective optimization for chemical engineering using harmony search. The main features of the HS method and several of its popular variants and hybrid versions including their relevant algorithm characteristics are described and discussed. A variety of global and multi-objective optimization problems from chemical engineering and their resolution using HS-based methods are also included. These problems involve thermodynamic calculations (phase stability analysis, phase equilibrium calculations, parameter estimation, and azeotrope calculation), heat exchanger design, distillation simulation, life cycle analysis, and water distribution systems, among others. Remarks on future developments of HS and its related algorithms for global and multi-objective optimization in chemical engineering are also provided in this review. HS is a reliable and promising stochastic optimizer to resolve challenging global and multi-objective optimization problems for process systems engineering.