In modern scientific research and engineering practice, mathematical formulas are often used to represent certain natural science laws. Ordinary ways of calculation have been difficult to satisfy those increasingly complex formulas. Using supercomputers for scientific computation can greatly improve computational efficiency. High performance computers can achieve a floating point operation speed of PFlops. They have been successfully applied in the fields of life sciences and personalized medicine, digital design and manufacturing, earth science and environmental engineering, smart city and materials science and engineering, and considerable achievement has been achieved. We briefly introduce high performance computer systems and summarize their application status and achievement in different fields.