Process capability analysis (PCA) that can be defined as the ability of any process to satisfy customer demands expressed via specification limits (SLs) is effectively utilized as an important function of statistical process control in order to examine process variability. PCA provides information about conforming and nonconforming production rates that indicate the amount of products that fall inside and outside of SLs, respectively. It is possible to classify processes as "capable" and "incapable" according to values of process capability indexes (PCIs). Therefore, PCA has a wide usage and critical effects on the manufacturing process. The fuzzy set theory can be successfully utilized in order to cope with vagueness and to add more flexibility and sensitiveness into traditional PCIs. For this aim, upper and lower specification limits can be expressed by means of linguistic variables. Fuzzy process capability indexes (FPCIs) can be produced by using fuzzy mean and fuzzy variance. There are many studies that utilized FPCIs for PCA in the literature. This study seeks to present a comprehensive literature review for publications related to FPCIs. These studies have been analyzed according to some features of them, such as year, document type, journal name, and country. Also, classifications including FPCI, application area, fuzzy parameters, and type of fuzzy sets have been presented in this study. Additionally, some statistical analyses have been conducted. As a result, we desired to provide a roadmap for researchers in this field and to present recent advances regarding FPCIs. The main aim of this article is to show possible future research areas on fuzzy PCA.