Alphaviruses are insect-borne viruses that cause serious and sometimes lethal infections in humans, and are also possible bioterrorism agents with the potential to produce widespread disease and societal disruption. There are currently no approved vaccines or antiviral drugs for humans to prevent or treat infections with alphaviruses. Small molecule libraries are often used to discover new antivirals, but they are limited by factors such as the costs of acquiring or maintaining large drug collections and the boundaries of synthetic and combinatorial chemistry. Thus, there is a pressing need for innovative approaches to antiviral drug discovery that go beyond the limits of synthetic chemistry. One approach takes advantage of the complex biosynthetic pathways of living organisms, which can produce natural products of nearly limitless structural diversity. Although major challenges exist in utilizing natural product resources for antiviral drug discovery, notable progress has been made recently. In this review, we provide an overview of alphavirus epidemiology, clinical disease, pathogenesis, molecular biology, and antiviral drug discovery, with an emphasis on the potential of natural product-derived resources as starting material for the identification of novel compounds to treat these virulent pathogens.