Ab initio protein structure prediction (PSP) models tertiary structures of proteins from its sequence. This is one of the most important and challenging problems in bioinformatics. In the last five decades, many algorithmic approaches have been made to solve the PSP problem. However, it remains unsolvable even for proteins of short sequence. In this review, the reported performances of various meta-heuristic algorithms were compared. Two of the algorithmic settings—protein representation and initialization functions were found to have definite positive influence on the running time and quality of structure. The hybrid of local search and genetic algorithm is recognized to be the best based on the performance. This work provides a chronicle brief on evolution of alternate attempts to solve the PSP problem, and subsequently discusses the merits and demerits of various meta-heuristic approaches to solve the PSP problem.