Functional peptides are short chain peptides composed of 2 to 50 amino acids, and their biological activities are closely related to their amino acid sequences, chain length, and structural architectures. Functional peptides can play a regulatory role in a variety of physiological processes by specifically recognizing and binding to target molecules in vivo. Due to their rapid action, strong specificity, less side effect and toxicity, functional peptides have shown great application potentials in many fields such as biomedicine, food science and cosmetics. For example, in the field of biomedicine, functional peptides can be used as the basic material of antimicrobe, anticancer, immune regulation and other therapeutic factors. In the food industry, they are used as natural supplements to enhance nutritional value for health benefit. In the field of cosmetics, functional peptides are widely used for the anti-aging, moisturizing, and repairing of the skin. In this paper, we discuss the ways of obtaining functional peptides, mainly including protein hydrolysis, chemical synthesis, and biosynthesis (e.g., through microbial recombinant expression technology), and compare their advantages and disadvantages and respective application scenarios. In terms of strategies for mining functional peptides, we review the latest research progress including phage surface display, machine learning algorithm, molecular docking and artificial intelligence. These techniques show significant potentials in the screening and design of functional peptides. In recent years, the rapid development of synthetic biology and the wide applications of bioinformatics and artificial intelligence have provided new ideas and strategies for the discovery and optimization of functional peptides, making it possible to screen functional peptides through machine learning and high throughput. Looking forward to the future, the research of functional peptides will face new challenges and opportunities. Improving the synthesis process for high efficiency, improving the stability of functional peptides through structural modifications, and using computer-aided optimization and artificial intelligence to design multifunctional peptides will become important research directions. At the same time, strengthening the safety and efficacy assessment of functional peptides can further enhance the applications of functional peptides.