The modern web stack, which is dominated by browser-based applications and API-first backends, now operates under an adversarial equilibrium where automated, AI-assisted attacks evolve continuously. Content Delivery Networks (CDNs) and edge computing place programmable defenses closest to users and bots, making them natural enforcement points for machine-learning (ML) driven inspection, throttling, and isolation. This survey synthesizes the landscape of AI-enhanced defenses deployed at the edge: (i) anomaly- and behavior-based Web Application Firewalls (WAFs) within broader Web Application and API Protection (WAAP), (ii) adaptive DDoS detection and mitigation, (iii) bot management that resists human-mimicry, and (iv) API discovery, positive security modeling, and encrypted-traffic anomaly analysis. We add a systematic survey method, a threat taxonomy mapped to edge-observable signals, evaluation metrics, deployment playbooks, and governance guidance. We conclude with a research agenda spanning XAI, adversarial robustness, and autonomous multi-agent defense. Our findings indicate that edge-centric AI measurably improves time-to-detect and time-to-mitigate while reducing data movement and enhancing compliance, yet introduces new risks around model abuse, poisoning, and governance.