This paper provides a systematic overview of catalyst research based on density functional theory (DFT), covering its theoretical foundations, applications, case studies, future perspectives, and challenges. It introduces the development of DFT, commonly used exchange-correlation functionals, and their applications in elucidating catalytic surface reaction mechanisms, identifying active sites, optimizing reaction selectivity, and designing nanocatalysts. Through specific case studies, this paper highlights the critical role of DFT in various catalytic reactions and examines the emerging integration of DFT with machine learning to enhance predictive accuracy and accelerate catalyst discovery. This study serves as a comprehensive reference for advancing research in this field.