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 filter out low quality data. This survey provides an overview of the face quality assessment literature in the framework of face biometrics, with a focus on face recognition based on visible wavelength face images as opposed to e.g. depth or infrared quality assessment. A trend towards deep learning based methods is observed, including notable conceptual differences among the recent approaches. 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.