A review article, containing information on the options, possibilities, and prospects for the development of antibacterial finishing of textile materials, is presented. A wide range of products designed to impart antibacterial, antimicrobial, and antiviral properties to textile materials is considered. The main factors determining the appropriate decision on the technological and functional choice of the protective composition are presented, including the nature of the fiber-forming polymer, the tasks that the resulting material is designed to solve, and its application options. Compositions providing the required effect of destruction of the pathogenic flora and their application technologies are described. Special attention is paid to antimicrobial agents based on silver nanoparticles. Nanoparticles of this metal have a detrimental effect on antibiotic-resistant strains of bacteria; their effectiveness is higher as compared to a number of well-known antibiotics, for example, penicillin and its analogues. Silver nanoparticles are harmless to the human body. Acting as an inhibitor, they limit the activity of the enzyme responsible for oxygen consumption by single-cell bacteria, viruses, and fungi. In this case, silver ions bind to the outer and inner proteins of the bacterial cell membranes, blocking cellular respiration and reproduction. Various options to apply microencapsulation methods for the implementation of antibacterial finishing are considered, including: phase separation, suspension crosslinking, simple and complex coacervation, spray drying, crystallization from the melt, evaporation of the solvent, co-extrusion, layering, fluidized bed spraying, deposition, emulsion and interphase polymerization, layer-by-layer electrostatic self-assembly etc. All presented technologies are at various development stages—from the laboratory stage to production tests, they all have certain advantages and disadvantages. The accelerated development and implementation of the described methods in production of textile materials is relevant and is related to the existing complex epidemiological situation in the world.