The ongoing COVID-19 pandemic caused by SARS-CoV-2 has significantly affected the world, creating a global health emergency. For controlling the virus spread, effective and reliable diagnostic and therapeutic measures are highly expected. Using proper biomedical materials to produce detection kits/devices and personal protective equipment (PPE), such as swabs and masks, has become the focus since they play critical roles in virus diagnostics and prevention. Electrospun polymer composites have garnered substantial interest due to their potential to provide antiviral healthcare solutions. In this review, we summarized the recent efforts in developing advanced antiviral electrospun polymer composites for virus detection and prevention. We highlighted some novel strategies for developing effective antiviral personal protective equipment (PPE), including self-sterilization, reusability, and potential antiviral drug encapsulation. Besides, we discussed the current challenges and future perspectives for improving the materials’ performance to achieve better virus detection, antiviral, prevention, and therapeutics.