The network motif (motif for short) is the smallest decomposable unit of a biological network or its smallest building block. It is an important research issue in systems biology. Motifs exist in various types of biological networks with information-processed functions. Simulations and experiments were carried out to study their dynamical properties. This paper reviews the styles and functions of motifs and the databases and tools to find motifs. The motifs we discuss in the paper include Negative Auto-Regulation(NAR), Positive Auto-Regulation (PAR), Forward Feedback Loop(FFL), Single Input Module(SIM), Multiple Input Modules (MIMs), regulator chain motifs, multi-component loop, bridge and brick motif in transcriptional networks, and motifs in signal transduction networks, as well as those in neural networks. The motifs might be viewed as the electric devices. This review also discusses the properties and the evolutions of network motifs, and related applications to synthetic biology. Finally, it is pointed out that the network motif study might be the first step in the studies of biological networks in systems biology to provide a good research method to study the module and synthetic biology. More types of motifs in various networks should be found out and more in-vivo experiments should be carried out. The further study might produce some general principles in biological networks.