Biodegradable polymers are promising materials for use in medical applications such as stents. Their properties are comparable to commercially available resistant metal and polymeric stents, which have several major problems, such as stent migration and stent clogging due to microbial biofilm. Consequently, conventional stents have to be removed operatively from the patient’s body, which presents a number of complications and can also endanger the patient’s life. Biodegradable stents disintegrate into basic substances that decompose in the human body, and no surgery is required. This review focuses on the specific use of stents in the human body, the problems of microbial biofilm, and possibilities of preventing microbial growth by modifying polymers with antimicrobial agents.