We present FACESEC, a framework for fine-grained robustness evaluation of face recognition systems. FACESEC evaluation is performed along four dimensions of adversarial modeling: the nature of perturbation (e.g., pixel-level or face accessories), the attacker’s system knowledge (about training data and learning architecture), goals (dodging or impersonation), and capability (tailored to individual inputs or across sets of these). We use FACESEC to study five face recognition systems in both closed-set and open-set settings, and to evaluate the state-of-the-art approach for defending against physically realizable attacks on these. We find that accurate knowledge of neural architecture is significantly more important than knowledge of the training data in black-box attacks. Moreover, we observe that open-set face recognition systems are more vulnerable than closed-set systems under different types of attacks. The efficacy of attacks for other threat model variations, however, appears highly dependent on both the nature of perturbation and the neural network architecture. For example, attacks that involve adversarial face masks are usually more potent, even against adversarially trained models, and the ArcFace architecture tends to be more robust than the others.