The innate immune system is the first line of the host defense program against pathogens and harmful substances. Antiviral innate immune responses can be triggered by multiple cellular receptors sensing viral components. The activated innate immune system produces interferons (IFNs) and cytokines that perform antiviral functions to eliminate invading viruses. Coronaviruses are single-stranded, positive-sense RNA viruses that have a broad range of animal hosts. Coronaviruses have evolved multiple means to evade host antiviral immune responses. Successful immune evasion by coronaviruses may enable the viruses to adapt to multiple species of host organisms. Coronavirus transmission from zoonotic hosts to humans has caused serious illnesses, such as severe acute respiratory syndrome (SARS), Middle East respiratory syndrome (MERS), and coronavirus disease-2019 (COVID-19), resulting in global health and economic crises. In this review, we summarize the current knowledge of the mechanisms underlying host sensing of and innate immune responses against coronavirus invasion, as well as host immune evasion strategies of coronaviruses.