Several biomolecular condensates assemble in mammalian cells in response to viral infection. The most studied of these are stress granules (SGs), which have been proposed to promote antiviral innate immune signaling pathways, including the RLR-MAVS, the protein kinase R (PKR), and the OAS-RNase L pathways. However, recent studies have demonstrated that SGs either negatively regulate or do not impact antiviral signaling. Instead, the SG-nucleating protein, G3BP1, may function to perturb viral RNA biology by condensing viral RNA into viral-aggregated RNA condensates, thus explaining why viruses often antagonize G3BP1 or hijack its RNA condensing function. However, a recently identified condensate, termed double-stranded RNA-induced foci, promotes the activation of the PKR and OAS-RNase L antiviral pathways. In addition, SG-like condensates known as an RNase L-induced bodies (RLBs) have been observed during many viral infections, including SARS-CoV-2 and several flaviviruses. RLBs may function in promoting decay of cellular and viral RNA, as well as promoting ribosome-associated signaling pathways. Herein, we review these recent advances in the field of antiviral biomolecular condensates, and we provide perspective on the role of canonical SGs and G3BP1 during the antiviral response.