Influenza viruses have affected the world for over a century, causing multiple pandemics. Throughout the years, many prophylactic vaccines have been developed for influenza; however, these viruses are still a global issue and take many lives. In this paper, we review influenza viruses, associated immunological mechanisms, current influenza vaccine platforms, and influenza infection, in the context of immunocompromised populations. This review focuses on the qualitative nature of immune responses against influenza viruses, with an emphasis on trained immunity and an assessment of the characteristics of the host–pathogen that compromise the effectiveness of immunization. We also highlight innovative immunological concepts that are important considerations for the development of the next generation of vaccines against influenza viruses.