Nanofibrous materials represent a very promising form of advanced carrier systems that can be used industrially, especially in regenerative medicine as highly functional bandages, or advanced wound dressings. By incorporation of antimicrobial additives directly into the structure of the nanofiber carrier, the functionality of the layer is upgraded, depending on the final requirement—bactericidal, bacteriostatic, antiseptic, or a generally antimicrobial effect. Such highly functional nanofibrous layers can be prepared mostly by electrospinning technology from both synthetic and natural polymers. The presence of a natural polymer in the composition is very advantageous. Especially in medical applications where, due to the presence of the material close to the human body, the healing process is more efficient and without the occurrence of an unwanted inflammatory response. However, converting natural polymers into nanofibrous form, with a homogeneously distributed and stable additive, is a great challenge. Thus, a combination of natural and synthetic materials is often used. This review clearly summarizes the issue of the incorporation and effectiveness of different types of antimicrobial substances, such as nanoparticles, antibiotics, common antiseptics, or substances of natural origin, into electrospun nanofibrous layers made of mostly natural polymer materials. A section describing the problematic aspects of antimicrobial polymers is also included.