In recent years, the study of partial synchronization of coupled oscillators in complex networks has attracted great attention. The underlying reason is both the extensive existence of the patterns of partial synchronization in brain network and their close relationship to brain functions of cognition and memory. In this paper, we briefly review the research progress in this field. According to the researches by different groups, we classify them as three types, i.e. chimera state, remote synchronization, and clustering synchronization. We mainly discuss the conditions of these three states, as well as their models, detections, and their applications in biology. We discuss the relationship among the three types of states and give some outlooks for future studies.