Due to the crisis of energy consumpticon and environmental pollution, developing high-efficiency and low-cost catalysts is especially crucial and demanded, and the related research is increasing rapidly. Between them, copper and copper-based compounds are broadly investigated, due to their excellent properties, including ability of absorbing visible light, electronic tunability through adjusting the type and ratio of the bonded element, high catalytic efficiency and recycling property, abundant in the earth, low cost and valuable facet engineering. In this chapter, we will first introduce the crystal and electronic structure of pure copper, including the bulk and various surfaces. Then, the electronic structure of copper-based compounds will be introduced, including CuOx, CuNx, CuSix, and so on, whose band structure can be tuned from metal to semiconductor, topological semimetal, and even superconductor. At last, the application and mechanism in catalysis will be introduced, including plasmonic catalysis, hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), nitrogen reduction reaction (NRR), carbon dioxide reduction reaction (CO2RR), and single-atom catalysis (SAC). We found that Cu element can be incorporated into a broad type of materials with novel electronic structures. Furthermore, Cu-based materials play a vital role in energy conversion and catalysis.