Textiles with antimicrobial functionality have been intensively and extensively investigated in the recent decades, mostly because they are present in everyday life in various applications: medicine and healthcare, sportswear, clothing and footwear, furniture and upholstery, air and water purification systems, food packaging etc. Their ability to kill or limit the growth of the microbial population in a certain context defines their activity against bacteria, fungi, and viruses, and even against the initial formation of the biofilm prior to microorganisms’ proliferation. Various classes of antimicrobials have been employed for these highly specialized textiles, namely, organic synthetic reagents and polymers, metals and metal oxides (micro- and nanoparticles), and natural and naturally derived compounds, and their activity and range of applications are critically assessed. At the same time, different modern processing techniques are reviewed in relation to their applications. This paper focuses on some advances and challenges in the field of antimicrobial textiles given their practical importance as it appears from the most recent reports in the literature.