The occurrence and spread of antimicrobial resistance (AMR) pose a looming threat to human health around the world. Novel antibiotics are urgently needed to address the AMR crisis. In recent years, antimicrobial peptides (AMPs) have gained increasing attention as potential alternatives to conventional antibiotics due to their abundant sources, structural diversity, broad-spectrum antimicrobial activity, and ease of production. Given its significance, there has been a tremendous advancement in the research and development of AMPs. Numerous AMPs have been identified from various natural sources (e.g., plant, animal, human, microorganism) based on either well-established isolation or bioinformatic pipelines. Moreover, computer-assisted strategies (e.g., machine learning (ML) and deep learning (DL)) have emerged as a powerful and promising technology for the accurate prediction and design of new AMPs. It may overcome some of the shortcomings of traditional antibiotic discovery and contribute to the rapid development and translation of AMPs. In these cases, this review aims to appraise the latest advances in identifying and designing AMPs and their significant antimicrobial activities against a wide range of bacterial pathogens. The review also highlights the critical challenges in discovering and applying AMPs.