Vision-language models (VLMs), spanning predictive architectures to generative Multimodal Large Language Models (MLLMs), have revolutionized artificial intelligence through powerful cross-modal alignment and zero-shot generalization. However, enabling them to learn continually from non-stationary data remains a major challenge, as their cross-modal alignment and generalization capabilities are particularly vulnerable to catastrophic forgetting. Unlike traditional unimodal continual learning (CL), VLMs face unique challenges such as cross-modal feature drift, parameter interference due to shared architectures, and zero-shot capability erosion. Furthermore, generative MLLMs exhibit a unique "alignment tax," where catastrophic forgetting manifests not merely as factual amnesia, but as a systemic collapse of deep Chain-of-Thought (CoT) reasoning. This survey presents the first comprehensive diagnostic review bridging continual learning across predictive VLMs and generative MLLMs. We systematically deconstruct the aforementioned failure modes and propose a challenge-driven taxonomy comprising four core paradigms: (1) Multi-Modal Replay Strategies addressing explicit and implicit memory drift; (2) Cross-Modal Regularization enforcing topological and geometric alignment; (3) Parameter-Efficient Adaptation utilizing dynamic routing and subspace projections; and the emerging (4) Model Fusion and Decoupling paradigms. We critically analyze the evolution of evaluation protocols, highlighting the essential shift toward dual-track benchmarks (Domain vs. Ability CL). Finally, we chart a roadmap for future research, emphasizing compositional zero-shot learning, embodied AI with sensor fusion, and autonomous agentic ecosystems. All resources are available at: https://github.com/YuyangSunshine/Awesome-Continual-learning-of-Vision-Language-Models

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