Depression is a pervasive global mental health disorder with significant societal impact. While AI-based audio-visual assessment tools offer a promising, objective, and scalable alternative to traditional diagnostics, their translation to clinical practice is blocked by a critical hurdle: trust. These tools must be demonstrably reliable, fair, explainable, and private. This paper provides a comprehensive review of the automated depression recognition field, uniquely framed through the lens of Trustworthy AI. We first survey the primary technical frameworks from unimodal handcrafted features to end-to-end multimodal fusion, establishing the technical foundation. We then conduct an in-depth analysis of the core pillars of trustworthiness, including explainability (moving from post-hoc visualization to interpretable-by-design methods), reliability and fairness (analyzing Uncertainty Quantification and the challenge of equitable reliability), and the non-trivial challenge of privacy (surveying approaches from intermediate features, Federated Learning, and hardware-level Deep Optics). We conclude that a holistic focus on trustworthiness, including generalization, multimodal explainability, and the privacy-efficacy trade-off, is the central challenge and the most critical direction for the field’s future.