Mammalian arenaviruses are zoonotic viruses that cause asymptomatic, persistent infections in their rodent hosts but can lead to severe and lethal hemorrhagic fever with bleeding and multiorgan failure in human patients. Lassa virus (LASV), for example, is endemic in several West African countries, where it is responsible for an estimated 500,000 infections and 5,000 deaths annually. There are currently no FDA-licensed therapeutics or vaccines available to combat arenavirus infection. A hallmark of arenavirus infection (e.g., LASV) is general immunosuppression that contributes to high viremia. Here, we discuss the early host immune responses to arenavirus infection and the recently discovered molecular mechanisms that enable pathogenic viruses to suppress host immune recognition and to contribute to the high degree of virulence. We also directly compare the innate immune evasion mechanisms between arenaviruses and other hemorrhagic fever-causing viruses, such as Ebola, Marburg, Dengue, and hantaviruses. A better understanding of the immunosuppression and immune evasion strategies of these deadly viruses may guide the development of novel preventative and therapeutic options.