The continuous spread of African swine fever virus (ASFV) in Europe and Asia represents a major threat to livestock health, with billions of dollars of income losses and major perturbations of the global pig industry. One striking feature of African swine fever (ASF) is the existence of different forms of the disease, ranging from acute with mortality rates approaching 100% to chronic, with mild clinical manifestations. These differences in pathogenicity have been linked to genomic alterations present in attenuated ASFV strains (and absent in virulent ones) and differences in the immune response of infected animals. In this mini-review, we summarized current knowledge on the connection between ASFV pathogenicity and the innate immune response induced in infected hosts, with a particular focus on the pathways involved in ASFV detection. Indeed, recent studies have highlighted the key role of the DNA sensor cGAS in ASFV sensing. We discussed what other pathways may be involved in ASFV sensing and inflammasome activation and summarized recent findings on the viral ASFV genes involved in the modulation of the interferon (IFN) and nuclear factor kappa B (NF-κB) pathways.