Most materials conventionally found in nature expand with an increase in temperature. In actual systems and assemblies like precision instruments, this can cause thermal distortions which can be difficult to handle. Materials with a tendency to shrink with an increase in temperature can be used alongside conventional materials to restrict the overall dimensional change of structures. Such structures, also called negative-thermal-expansion materials, could be crucial in applications like electronics, biomedicine, aerospace components, etc., which undergo high changes in temperature. This can be achieved using mechanically engineered materials, also called negative thermal expansion (NTE) mechanical metamaterials. Mechanical metamaterials are mechanically architected materials with novel properties that are rare in naturally occurring materials. NTE metamaterials utilize their artificially engineered architecture to attain the rare property of negative thermal expansion. The emergence of additive manufacturing has enabled the feasible production of their intricate architectures. Industrial processes such as laser powder bed fusion and direct energy deposition, both utilized in metal additive manufacturing, have proven successful in creating complex structures like lattice formations and multimaterial components in the industrial sector, rendering them suitable for manufacturing NTE structures. Nevertheless, this review examines a range of fabrication methods, encompassing both additive and traditional techniques, and explores the diverse materials used in the process. Despite NTE metamaterials being a prominent field of research, a comprehensive review of these architected materials is missing in the literature. This article aims to bridge this gap by providing a state-of-the-art review of these metamaterials, encompassing their design, fabrication, and cutting-edge applications.