African swine fever (ASF), a highly infectious and devastating disease affecting both domestic pigs and wild boars, is caused by the African swine fever virus (ASFV). ASF has resulted in rapid global spread of the disease, leading to significant economic losses within the swine industry. A significant obstacle to the creation of safe and effective ASF vaccines is the existing knowledge gap regarding the pathogenesis of ASFV and its mechanisms of immune evasion. The cyclic GMP–AMP synthase (cGAS)–stimulator of interferon genes (STING) pathway is a major pathway mediating type I interferon (IFN) antiviral immune response against infections by diverse classes of pathogens that contain DNA or generate DNA in their life cycles. To evade the host’s innate immune response, ASFV encodes many proteins that inhibit the production of type I IFN by antagonizing the cGAS-STING signaling pathway. Multiple proteins of ASFV are involved in promoting viral replication by protein–protein interaction during ASFV infection. The protein QP383R could impair the function of cGAS. The proteins EP364R, C129R and B175L could disturb the function of cyclic guanosine monophosphate-adenosine monophosphate (cGAMP). The proteins E248R, L83L, MGF505-11R, MGF505-7R, H240R, CD2v, E184L, B175L and p17 could interfere with the function of STING. The proteins MGF360-11L, MGF505-7R, I215L, DP96R, A151R and S273R could affect the function of TANK Binding Kinase 1 (TBK1) and IκB kinase ε (IKKε). The proteins MGF360-14L, M1249L, E120R, S273R, D129L, E301R, DP96R, MGF505-7R and I226R could inhibit the function of Interferon Regulatory Factor 3 (IRF3). The proteins MGF360-12L, MGF505-7R/A528R, UBCv1 and A238L could inhibit the function of nuclear factor kappa B (NF-Κb).