With the increasingly accumulated data from high-throughput technologies, study on biomolecular networks has become one of key focuses in systems biology and bioinformatics. In particular, various types of molecular networks (e.g., protein-protein interaction (PPI) network; gene regulatory network (GRN); metabolic network (MN); gene coexpression network (GCEN)) have been extensively investigated, and those studies demonstrate great potentials to discover basic functions and to reveal essential mechanisms for various biological phenomena, by understanding biological systems not at individual component level but at a system-wide level. Recent studies on networks have created very prolific researches on many aspects of living organisms. In this paper, we aim to review the recent developments on topics related to molecular networks in a comprehensive manner, with the special emphasis on the computational aspect. The contents of the survey cover global topological properties and local structural characteristics, network motifs, network comparison and query, detection of functional modules and network motifs, function prediction from network analysis, inferring molecular networks from biological data as well as representative databases and software tools.