Negative thermal expansion (NTE) upon heating is an unusual property but is observed in many materials over varying ranges of temperature. A brief review of mechanisms for NTE and prominent materials will be presented here. Broadly there are two basic mechanisms for intrinsic NTE within a homogenous solid; structural and electronic. Structural NTE is driven by transverse vibrational motion in insulating framework-type materials e.g., ZrW2O8 and ScF3. Electronic NTE results from thermal changes in electronic structure or magnetism and is often associated with phase transitions. A classic example is the Invar alloy, Fe0.64Ni0.36, but many exotic mechanisms have been discovered more recently such as colossal NTE driven by Bi-Ni charge transfer in the perovskite BiNiO3. In addition there are several types of NTE that result from specific sample morphologies. Several simple materials, e.g., Au, CuO, are reported to show NTE as nanoparticles but not in the bulk. Microstructural enhancements of NTE can be achieved in ceramics of materials with anisotropic thermal expansion such as beta-eucryptite and Ca2RuO4, and artificial NTE metamaterials can be fabricated from engineered structures of normal (positive) thermal expansion substances.