At the end of the 20th century, the discovery of the characteristics of complex networks, such as small world and scale-freeness, brought unprecedented attention and development in the structural characteristics, dynamics, group games, decision-making, and control of various complex systems in the early 21st century. Given the effectiveness of complex networks in characterizing the underlying topology of complex systems, here we first introduce several representative models and methods for constructing synthetic static complex networks with essential characteristics. Such models and methods change the state of constructing complex networks from individuals' limited and high-cost empirical interaction data, and thus provide an effective solution for constructing static networks for researchers in multiple fields to further explore related scientific issues. In recent years, with the continuous improvement of the ability to collect massive high-precision interaction data of individuals, it is possible to construct temporal networks, which dynamically evolve over time. As an essential feature of temporal networks, the inter-event time of interactions often presents a power-law distribution, namely, the bursty behavior. Existing results have shown that the bursty behavior may significantly change the information dissemination, game, decision-making, and control of temporal networks. We further summarize the parameter estimation method for testing the power-law distribution of empirical individuals' interaction data, and introduce the Poisson process and queuing system, and present typical theories and methods for constructing various temporal networks.