Non-Hermitian systems have attracted much attention during the past few years. NonHermitian terms can be introduced into the model Hamiltonian to give a good description of open systems. The presence of such terms will modify the system's properties in a significant way, leading to phenomena that cannot be found in Hermitian systems, such as the exceptional point, the nonHermitian skin effect, etc. These exotic effects are not only important in theoretical studies, they are potential for applications in designing new types of quantum sensors and lasers. Based on the authors' recent research work on non-Hermitian physics, this paper summarizes the recent progress on onedimensional non-Hermitian systems with asymmetric hopping.