Acoustic metamaterials (AMs) composed of periodic artificial structures have extraordinary sound wave manipulation capabilities compared with traditional acoustic materials, and they have attracted widespread research attention. The sound insulation performance of thin-walled structures commonly used in engineering applications with restricted space, for example, vehicles’ body structures, and the latest studies on the sound insulation of thin-walled metamaterial structures, are comprehensively discussed in this paper. First, the definition and math law of sound insulation are introduced, alongside the primary methods of sound insulation testing of specimens. Secondly, the main sound insulation acoustic metamaterial structures are summarized and classified, including membrane-type, plate-type, and smart-material-type sound insulation metamaterials, boundaries, and temperature effects, as well as the sound insulation research on composite structures combined with metamaterial structures. Finally, the research status, challenges, and trends of sound insulation metamaterial structures are summarized. It was found that combining the advantages of metamaterial and various composite panel structures with optimization methods considering lightweight and proper wide frequency band single evaluator has the potential to improve the sound insulation performance of composite metamaterials in the full frequency range. Relative review results provide a comprehensive reference for the sound insulation metamaterial design and application.