The Efficient SMT-Based Context-Bounded Model Checker (ESBMC) has grown from a research prototype for verifying embedded ANSI-C software into one of the most versatile and industrially capable formal verification platforms available today. Since its first publication in 2009, ESBMC has undergone persistent evolution: expanding its verification techniques, widening its language support to nine front-ends, integrating industrial-strength SMT solvers, and - most recently - coupling with Large Language Models (LLMs) and autonomous AI agents. This survey traces the full trajectory of ESBMC from its original design principles to the state of the art in 2025-2026, documenting 43 awards at SV-COMP and Test-Comp, peer recognition at leading software engineering venues, including a Distinguished Paper Awards at ICSE'11 and ASE'24, a Most Influential Paper Award at ASE'23, and a Best Tool Paper Award at SBSeg'23, its role as a formal verification backend for LLM-driven self-healing software and loop invariant generation, and the first industrial deployment of an integrated agentic model-checking architecture through the NVIDIA-OpenSMA framework, establishing ESBMC as a natively autonomous verification kernel rather than a passive validation backend. We synthesize its economic impact - over GBP 9.3 million and EUR 4.98 million in confirmed public research funding, the VeriBee spin-off, and a defense industrial deployment at Lockheed Martin - and conclude with a structured agenda of open challenges spanning scalability, neurosymbolic verification, counterexample intelligibility, cross-language verification, safety standards compliance, and open-source sustainability.