Abstract: Plasma is a complex system composed of a large number of charged and neutral particles, which has wide applications in industrial fields such as power and energy. The study of plasma characteristics is the basis for improving the performance of important industrial equipment such as power equipment reliability and energy gain of nuclear fusion devices. However, it is difficult to accurately measure the internal parameters of plasma through experimental methods, and traditional numerical simulations often face challenges such as high computational costs and low efficiency. In recent years, the development of deep neural networks has provided new directions for breaking through this dilemma, but traditional deep learning methods remain limited in addressing highly nonlinear and strongly coupled plasma systems. In contrast, emerging deep neural operator networks have demonstrated unique advantages in modeling complex physical systems due to their ability to model functional mappings. Starting from the study of plasma characteristics, the fundamental research methods are first introduced, then mainstream neural operator frameworks are systematically reviewed, and finally recent advances in the application of such methods to plasma experimental diagnosis and numerical simulation are summarized, aiming to provide new insights and methodological pathways for plasma characteristic research based on deep neural operator networks.