The development of bacterial resistance to antimicrobial drugs is a major challenge in the clinical treatment of infectious diseases and has received widespread attention. Bacteria acquire resistance through a variety of mechanisms to evade killing by antimicrobial drugs. Phage is a generic term for bacteriophage that infects microorganisms such as bacteria, fungi, actinomycetes or spirochetes. Its application in the treatment of infectious diseases with drug-resistant bacteria in clinical settings has achieved some success in recent years, but the ensuing problem of phage resistance has limited its application. This paper reviews the main mechanisms of bacterial drug resistance and phage resistance, and the main current advances in synthetic biology in addressing bacterial resistance to antibiotics and resistance to natural phages.