In the real world, reconciling a choice between multiple conflicting objectives is a common problem. Solutions to a multi-objective problem are those that have the best possible negotiation given the objectives. An evolutionary algorithm called Particle swarm optimization is used to find a solution from the solution space. It is a population-based optimization technique that is effective, efficient, and easy to implement. Changes in the particle swarm optimization technique are required in order to get solutions to a multi-objective optimization problem. Therefore, this paper provides the proper concept of particle swarm optimization and the multi-objective optimization problem in order to build a basic background with which to conduct multi-objective particle swarm optimization. Then, we discuss multi-objective particle swarm optimization concepts. Multi-objective particle swarm optimization techniques and some of the most important future research directions are also included.