|The performance of face analysis and recognition systems depends on the quality of the acquired face data, which is influenced by numerous factors. Automatically assessing the quality of face data in terms of biometric utility can thus be useful to detect low-quality data and make decisions accordingly. This survey provides an overview of the face image quality assessment literature, which predominantly focuses on visible wavelength face image input. A trend towards deep learning based methods is observed, including notable conceptual differences among the recent approaches, such as the integration of quality assessment into face recognition models. Besides image selection, face image quality assessment can also be used in a variety of other application scenarios, which are discussed herein. Open issues and challenges are pointed out, i.a. highlighting the importance of comparability for algorithm evaluations, and the challenge for future work to create deep learning approaches that are interpretable in addition to providing accurate utility predictions.