In this paper, an important idea of devising a quantum algorithm is introduced, based on the description and analysis of two classes of quantum search algorithms, i.e. the unstructured search algorithms and structured search algorithms. Some qualities of Grover’s search algorithm, which is the representation of the unstructured search algorithms are introduced and summarized, by analyzing its peculiar complexity, completeness, sensitivity to the errors in the mappings, and its advantages and disadvantages. On introducing structure-based search algorithm, the Tad Hogg’s series of search algorithms are referred to. They can be summarized into one universal algorithm framework, which can be separated into two parts, i.e., the problem-independent mapping and phase rotation matrix. This paper places emphasis on analyzing one of the phase adaptation strategies, and interprets how it works and what can make it more efficient. Some other factors affect the algorithm are also discussed more generally. Finally, based on the comparison and analysis of classical search algorithm and the quantum one, the thoughts behind various quantum search algorithms are illustrated.