Kaposi’s sarcoma-associated herpesvirus (KSHV) and the Epstein–Barr virus (EBV) are double-stranded DNA oncogenic gammaherpesviruses. These two viruses are associated with multiple human malignancies, including both B and T cell lymphomas, as well as epithelial- and endothelial-derived cancers. KSHV and EBV establish a life-long latent infection in the human host with intermittent periods of lytic replication. Infection with these viruses induce the expression of both viral and host RNA transcripts and activates several RNA sensors including RIG-I-like receptors (RLRs), Toll-like receptors (TLRs), protein kinase R (PKR) and adenosine deaminases acting on RNA (ADAR1). Activation of these RNA sensors induces the innate immune response to antagonize the virus. To counteract this, KSHV and EBV utilize both viral and cellular proteins to block the innate immune pathways and facilitate their own infection. In this review, we summarize how gammaherpesviral infections activate RNA sensors and induce their downstream signaling cascade, as well as how these viruses evade the antiviral signaling pathways to successfully establish latent infection and undergo lytic reactivation.