The key to achieving autonomous driving lies in topology-aware perception, the structured understanding of the driving environment with an emphasis on lane topology and road semantics. This survey systematically reviews four core research directions under this theme: vectorized map construction, topological structure modeling, prior knowledge fusion, and language model-based perception. Across these directions, we observe a unifying trend: a paradigm shift from static, pre-built maps to dynamic, sensor-driven perception. Specifically, traditional static maps have pro-vided semantic context for autonomous systems. However, they are costly to construct, difficult to update in real time, and lack generalization across regions, limiting their scal-ability. In contrast, dynamic representations leverage on-board sensor data for real-time map construction and topol-ogy reasoning. Each of the four research directions con-tributes to this shift through compact spatial modeling, se-mantic relational reasoning, robust domain knowledge in-tegration, and multimodal scene understanding powered by pre-trained language models. Together, they pave the way for more adaptive, scalable, and explainable autonomous driving systems.