<p>Hierarchical Adaptive Structured Mesh (HASM) video coding is a geometry-driven paradigm inspired by mesh-based modeling and dynamic tessellation principles applied to video compression. Unlike traditional block-based hybrid codecs such as MPEG-2, H.264/AVC, HEVC, and VVC, HASM adopts a content-adaptive mesh representation of video frames, enabling continuous motion modeling, reduced blocking artifacts, scalable refinement characteristics, and improved deformation fidelity in non-rigid motion scenarios. The technique models motion regions using hierarchical triangular or quadrilateral mesh structures whose vertices are adaptively refined according to scene complexity, motion gradients, or perceptual saliency. This paper presents a structured and systematic survey of HASM-based video coding research, spanning pioneering works of the late 1990s through contemporary neural-mesh hybrid systems and dynamic mesh coding frameworks. More than 200 referenced works are synthesized through a transparent literature selection protocol. The survey analyzes algorithmic foundations, hierarchical refinement strategies, affine motion modeling, rate–distortion behavior, VLSI realizations, integration with deep neural motion models, and applications in immersive and volumetric video environments. While several studies report measurable gains in low-bitrate deformation-heavy content compared to legacy block-based standards, performance remains scene dependent and large-scale standardized benchmarking against modern codecs remains limited. The survey critically evaluates computational complexity, occlusion handling, standardization challenges, and hardware feasibility. Future directions include mesh-constrained neural deformation fields, graph-transform motion modeling, occlusion-aware adaptive topology evolution, and hybrid geometry–neural compression systems.</p>