Antimicrobial resistance (AMR) developed by microorganisms is considered one of the most critical public health issues worldwide. This problem is affecting the lives of millions of people and needs to be addressed promptly. Mainly, antibiotics are the substances that contribute to AMR in various strains of bacteria and other microorganisms, leading to infectious diseases that cannot be effectively treated. To avoid the use of antibiotics and similar drugs, several approaches have gained attention in the fields of materials science and engineering as well as pharmaceutics over the past five years. Our focus lies on the design and manufacture of polymeric-based materials capable of incorporating antimicrobial agents excluding the aforementioned substances. In this sense, two of the emerging techniques for materials fabrication, namely, electrospinning and 3D printing, have gained significant attraction. In this article, we provide a summary of the most important findings that contribute to the development of antimicrobial systems using these technologies to incorporate various types of nanomaterials, organic molecules, or natural compounds with the required property. Furthermore, we discuss and consider the challenges that lie ahead in this research field for the coming years.