Antimicrobial resistance has become a critical global health problem due to the abuse of conventional antibiotics and the rise of multi-drug-resistant microbes. Antimicrobial peptides (AMPs) are a group of natural peptides that show promise as next-generation antibiotics due to their low toxicity to the host, broad spectrum of biological activity, including antibacterial, antifungal, antiviral, and anti-parasitic activities, and great therapeutic potential, such as anticancer, anti-inflammatory, etc. Most importantly, AMPs kill bacteria by damaging cell membranes using multiple mechanisms of action rather than targeting a single molecule or pathway, making it difficult for bacterial drug resistance to develop. However, experimental approaches used to discover and design new AMPs are very expensive and time-consuming. In recent years, there has been considerable interest in using in silico methods, including traditional machine learning (ML) and deep learning (DL) approaches, to drug discovery. While there are a few papers summarizing computational AMP prediction methods, none of them focused on DL methods. In this review, we aim to survey the latest AMP prediction methods achieved by DL approaches. First, the biology background of AMP is introduced, then various feature encoding methods used to represent the features of peptide sequences are presented. We explain the most popular DL techniques and highlight the recent works based on them to classify AMPs and design novel peptide sequences. Finally, we discuss the limitations and challenges of AMP prediction.