Based on the latest progress in superconductivity research, the authors form a conventional theory of superconductivity and express BCS paring theory at a higher level. They especially emphasis the importance of the long-range phase coherence for the superconductivity. They also point out some misunderstandings of basic concepts about superconductivity in present textbooks and monographs. They illustrate the correct theory of the high-Tc superconductivity and the application of the high-Tc superconductors to establish a correct and detailed theory regarding this mechanism in different systems.