The research of random signal sampling has become one of the mainstream directions in sampling theory in the past few decades, it has been widely concerned in the field of information and mathematics in both theory and practical application. In recent years, a series of research results on local average sampling of random processes and random fields have been obtained in the sampling theory. Firstly, the defects and limitations of sampling theorem in its application are analyzed. Secondly, the development and related results for the local average sampling theorem of stochastic process, multidimensional stochastic process,random field and spatio-temporal random field are introduced systematically. Finally, the further research directions of the spatiotemporal random field sampling problem are pointed out. The results show that the local average sampling method improves the sampling accuracy and approximation effect, and the random field local average sampling theory has important applications in wave parameter inversion and marine pollution monitoring. In particular, the research of the spatiotemporal random field sampling theory based on mixed norm not only has important theoretical value, but also has application value in engineering field.