Metamaterials, commonly known as synthetic composites with exotic dynamic characteristics, have recently generated increasing interest. A short description of composite metamaterial and their types, applications, and manufacturing techniques was reported. Contrary to all previous research, this investigation focuses on the recent studies of static and dynamic analysis of composite metamaterial structure and mechanical performance using experimental and finite element method analyses. Furthermore, the literature has described several methods for constructing composite sandwiches, properties, and advantages over conventional materials. Due to the wide variety of materials and configurations used in the final product, there is a corresponding diversity in manufacturing techniques. Therefore, the current research has mainly concentrated on a wealth of information that should be important to all researchers interested in keeping up with the most recent developments in composite metamaterial sandwich structures. Consequently, this study can be considered a guideline for researchers who intend further research on the mechanical behavior analysis and technology of designed composite metamaterial structures.