Functional magnetic resonance imaging (fMRI) has been a popular approach in brain research over the past 20 years. It offers a noninvasive method to probe the brain and uses blood oxygenation level dependent (BOLD) signal changes to access brain function. However, the BOLD signal only represents a small fraction of the total MR signal. System instability and various noise have a strong impact on the BOLD signal. Additionally, fMRI applies fast imaging technique to record brain cognitive process over time, requiring high temporal stability of MR scanners. Furthermore, data acquisition, image quality, processing, and statistical analysis methods also have a great effect on the results of fMRI studies. Quality assurance (QA) programs for fMRI can test the stability of MR scanners, evaluate the quality of fMRI and help to find errors during fMRI scanning, thereby greatly enhancing the success rate of fMRI. In this review, we focus on previous studies which developed QA programs and methods in SCI/SCIE citation peer-reviewed publications over the last 20 years, including topics on existing fMRI QA programs, QA phantoms, image QA metrics, quality evaluation of existing preprocessing pipelines and fMRI statistical analysis methods. The summarized studies were classified into four categories: QA of fMRI systems, QA of fMRI data, quality evaluation of data processing pipelines and statistical methods and QA of task-related fMRI. Summary tables and figures of QA programs and metrics have been developed based on the comprehensive review of the literature.