An effective innate antiviral response is critical for the mitigation of severe disease and host survival following infection. In vivo, the innate antiviral response is triggered by cells that detect the invading pathogen and then communicate through autocrine and paracrine signaling to stimulate the expression of genes that inhibit viral replication, curtail cell proliferation, or modulate the immune response. In other words, the innate antiviral response is complex and dynamic. Notably, in the laboratory, culturing viruses and assaying viral life cycles frequently utilizes cells that are derived from tissues other than those that support viral replication during natural infection, while the study of viral pathogenesis often employs animal models. In recapitulating the human antiviral response, it is important to consider that variation in the expression and function of innate immune sensors and antiviral effectors exists across species, cell types, and cell differentiation states, as well as when cells are placed in different contexts. Thus, to gain novel insight into the dynamics of the host response and how specific sensors and effectors impact infection kinetics by a particular virus, the model system must be selected carefully. In this review, we briefly introduce key signaling pathways involved in the innate antiviral response and highlight how these differ between systems. We then review the application of tissue-engineered or 3D models for studying the antiviral response, and suggest how these in vitro culture systems could be further utilized to assay physiologically-relevant host responses and reveal novel insight into virus-host interactions.