African swine fever (ASF) is an acute and highly contagious disease that causes severe economic losses to the swine industry.  ASF is caused by infection of African swine fever virus (ASFV) in domestic pigs, leading to almost 100% mortality.  However, no effective vaccines and pharmacologic treatment against ASF are available.  ASF poses a severe threat to the swine industry and the economy.  Here we summarize potential virus-host cell interaction mechanisms involving the suppression of innate and adaptive immune responses to ASFV entry and infection.  These mechanisms include modulation of apoptosis, inhibition of inflammatory responses, reduction of IFN production, inhibition of autophagy, and suppression of MHC-I expression.  Insights into immunoevasion strategies by ASFV may shed light on the development of vaccines, as well as preventive and therapeutic drugs.