This paper offers a review of univariate and multivariate process capability indices (PCIs). PCIs are statistic indicators widely used in the industry to quantify the capability of production processes by relating the variability of the measures of the product characteristics with the admissible one. Univariate PCIs involve single-product characteristics while multivariate PCIs deal with the multivariate case. When analyzing the capability of processes, decision makers of the industry may choose one PCI among all the PCIs existing in the literature depending on different criteria. In this article, we describe, cluster, and discuss univariate and multivariate PCIs. To cluster the PCIs, we identify three classes of characteristics: in the first class, the characteristics related to the information of the process data input are included; the second class includes characteristics related to the approach used to calculate the PCIs; and in the third class, we find characteristics related to the information that the PCIs give. We discuss the strengths and weaknesses of each PCI using four criteria: calculation complexity, globality of the index, relation to proportion of nonconforming parts, and robustness of the index. Finally, we propose a framework that may help practitioners and decision makers of the industry to select PCIs.