Silver nanoparticles (AgNPs) are a promising tool in the fight against pathogenic microorganisms. “Green” nanoparticles are especially valuable due to their environmental friendliness and lower energy consumption during production, as well as their ability to minimize the number of toxic by-products. This review focuses on the features of AgNP synthesis using living organisms (bacteria, fungi, plants) and the involvement of various biological compounds in this process. The mechanism of antibacterial activity is also discussed in detail with special attention given to anti-biofilm and anti-quorum sensing activities. The toxicity of silver nanoparticles is considered in light of their further biomedical applications.