Influenza A viruses (IAVs) evade the immune system of the host by several regulatory mechanisms. Their genomes consist of eight single-stranded segments, including nonstructural proteins (NS), basic polymerase 1 (PB1), basic polymerase 2 (PB2), hemagglutinin (HA), acidic polymerase (PA), matrix (M), neuraminidase (NA), and nucleoprotein (NP). Some of these proteins are known to suppress host immune responses. In this review, we discuss the roles, functions and underlying strategies adopted by IAV proteins to escape the host immune system by targeting different proteins in the interferon (IFN) signaling pathway, such as tripartite motif containing 25 (TRIM25), inhibitor of nuclear factor κB kinase (IKK), mitochondrial antiviral signaling protein (MAVS), Janus kinase 1 (JAK1), type I interferon receptor (IFNAR1), interferon regulatory factor 3 (IRF3), IRF7, and nuclear factor-κB (NF-κB). To date, the IAV proteins NS1, NS2, PB1, PB1-F2, PB2, HA, and PA have been well studied in terms of their roles in evading the host immune system. However, the detailed mechanisms of NS3, PB1-N40, PA-N155, PA-N182, PA-X, M42, NA, and NP have not been well studied with respect to their roles in immune evasion. Moreover, we also highlight the future perspectives of research on IAV proteins.