With the evolution of the industry, the production process becomes a large-scale problem that made scheduling jobs process as a combinatorial optimization problem. The most important and most common scheduling problem was the flow-shop scheduling problem and was considered an NP-hard problem. There are different variants of flow-shop scheduling problems such as permutation, non-permutation, no-idle, nowait, and hybrid flow shop scheduling problems. Permutation Flow-shop Scheduling problem (PFSP) is the most important variant of flow-shop problem, where its objective was to find the optimal or near to optimal sequence of n jobs on m machines with some criterion under some conditions. In this paper, it will be reviewed the PFSP with makespan criteria (completion time) and its mathematical model. Also, most of methods that used for solving PFSP will be reviewed and discussed in this paper, where each algorithm has different methodology for solving PFSP. There are three categories used for solving PFSP as traditional algorithms, heuristic algorithms, and meta-heuristic algorithms. This study concentrated on meta-heuristic algorithms in solving PFSP, due to its efficiency in solving many applications. From this study, it has been proved that meta-heuristic algorithms are playing a vital role in solving permutation flow-shop scheduling problem and it has attracted the attention of researchers in the past few years.