Swine Influenza A Virus (IAV-S) imposes a significant impact on the pork industry and has been deemed a significant threat to global public health due to its zoonotic potential. The most effective method of preventing IAV-S is vaccination. While there are tremendous efforts to control and prevent IAV-S in vulnerable swine populations, there are considerable challenges in developing a broadly protective vaccine against IAV-S. These challenges include the consistent diversification of IAV-S, increasing the strength and breadth of adaptive immune responses elicited by vaccination, interfering maternal antibody responses, and the induction of vaccine-associated enhanced respiratory disease after vaccination. Current vaccination strategies are often not updated frequently enough to address the continuously evolving nature of IAV-S, fail to induce broadly cross-reactive responses, are susceptible to interference, may enhance respiratory disease, and can be expensive to produce. Here, we review the challenges and current status of universal IAV-S vaccine research. We also detail the current standard of licensed vaccines and their limitations in the field. Finally, we review recently described novel vaccines and vaccine platforms that may improve upon current methods of IAV-S control.