This review highlights the different modes of synthesizing silver nanoparticles (AgNPs) from their elemental state to particle format and their mechanism of action against multidrug-resistant and biofilm-forming bacterial pathogens. Various studies have demonstrated that the AgNPs cause oxidative stress, protein dysfunction, membrane disruption, and DNA damage in bacteria, ultimately leading to bacterial death. AgNPs have also been found to alter the adhesion of bacterial cells to prevent biofilm formation. The benefits of using AgNPs in medicine are, to some extent, counter-weighted by their toxic effect on humans and the environment. In this review, we have compiled recent studies demonstrating the antibacterial activity of AgNPs, and we are discussing the known mechanisms of action of AgNPs against bacterial pathogens. Ongoing clinical trials involving AgNPs are briefly presented. A particular focus is placed on the mechanism of interaction of AgNPs with bacterial biofilms, which are a significant pathogenicity determinant. A brief overview of the use of AgNPs in other medical applications (e.g., diagnostics, promotion of wound healing) and the non-medical sectors is presented. Finally, current drawbacks and limitations of AgNPs use in medicine are discussed, and perspectives for the improved future use of functionalized AgNPs in medical applications are presented.