Dengue is a major public health issue in tropical and subtropical regions worldwide. The four serotypes of dengue virus (DENV1-DENV4) are spread primarily by Aedes aegypti and Aedes albopictus mosquitoes, whose geographic range continues to expand. Humans are the only host for epidemic strains of DENV, and the virus has developed sophisticated mechanisms to evade human innate immune responses. The host cell's first line of defense begins with an intracellular signaling cascade resulting in production of interferon α/β (IFN-α/β), which promotes intracellular antiviral responses and helps initiates the adaptive response during the course of DENV infection. In response, DENV has developed numerous ways to subvert these intracellular antiviral responses and directly inhibit cellular signaling cascades. Specifically, DENV manipulates the unfolded protein response and autophagy to counter cellular stress and delay apoptosis. The DENV non-structural protein NS4B and subgenomic flavivirus RNA interfere with the RNA interference pathway by inhibiting the RNase Dicer. During heterotypic secondary DENV infection, subneutralizing antibodies can enable viral uptake through Fcγ receptors and down-regulate signaling cascades initiated via the pattern recognition receptors TLR-3 and MDA5/RIG-I, thus reducing the antiviral state of the cell. The DENV NS2B/3 protein cleaves human STING/MITA, interfering with induction of IFN-α/β. Finally, DENV NS2A, NS4A, and NS4B complex together to block STAT1 phosphorylation, while NS5 binds and promotes degradation of human STAT2, thus preventing formation of the STAT1/STAT2 heterodimer and its transcriptional induction of interferon stimulating genes. Here, we discuss the host innate immune response to DENV and the mechanisms of immune evasion that DENV has developed to manipulate cellular antiviral responses.