Architectural backdoors pose an under-examined but critical threat to deep neural networks, embedding malicious logic directly into a model's computational graph. Unlike traditional data poisoning or parameter manipulation, architectural backdoors evade standard mitigation techniques and persist even after clean retraining. This survey systematically consolidates research on architectural backdoors, spanning compiler-level manipulations, tainted AutoML pipelines, and supply-chain vulnerabilities. We assess emerging detection and defense strategies, including static graph inspection, dynamic fuzzing, and partial formal verification, and highlight their limitations against distributed or stealth triggers. Despite recent progress, scalable and practical defenses remain elusive. We conclude by outlining open challenges and proposing directions for strengthening supply-chain security, cryptographic model attestations, and next-generation benchmarks. This survey aims to guide future research toward comprehensive defenses against structural backdoor threats in deep learning systems.