Genes that are thought to be critical for the survival of organisms or cells are called essential genes. The prediction of essential genes and their products (essential proteins) is of great value in exploring the mechanism of complex diseases, the study of the minimal required genome for living cells and the development of new drug targets. As laboratory methods are often complicated, costly and time-consuming, a great many of computational methods have been proposed to identify essential genes/proteins from the perspective of the network level with the in-depth understanding of network biology and the rapid development of biotechnologies. Through analyzing the topological characteristics of essential genes/proteins in protein-protein interaction networks (PINs), integrating biological information and considering the dynamic features of PINs, network-based methods have been proved to be effective in the identification of essential genes/proteins. In this paper, we survey the advanced methods for network-based prediction of essential genes/proteins and present the challenges and directions for future research.