In the evolution process of humans, nature has played an important role in the transformation of mathematical investigation knowledge to modern human technological advancement. Nature optimizes the work based on biological, physical and chemical principles integrated with numerous mathematical models. People have learned the different principle and structure to design optimization algorithm that has been widely used in theoretical analysis and practical applications. In this chapter, we try to review several common nature-inspired algorithms with analysis systematically. Also, we try to incorporate the standard benchmark functions that are needed to evaluate the optimization algorithm. Through the chapter, we will discuss the original principle and the diversity of the algorithm in different practical applications.