Zoonotic spillover of influenza A viruses into humans has repeatedly triggered pandemics throughout history. Since their emergence in the 1990s, H5N1 influenza viruses have significantly expanded their geographical range and host species, raising global concern about the potential for sustained human-to-human transmission. In this review, we examine the virological characteristics of currently circulating H5N1 strains, key molecular barriers limiting their spread among humans, and critical areas of future research to mitigate the ongoing H5N1 panzootic and prevent future pandemics.