Chalcones are naturally occurring open-chain flavonoids widely distributed in plants and recognized for their broad spectrum of pharmacological activities. Their versatile scaffold allows for extensive structural modifications, leading to a diverse range of natural and synthetic derivatives with notable biological potential. In the context of viral infections, chalcones have demonstrated remarkable efficacy against a variety of human pathogens, including dengue virus, HIV, HCV, influenza A, SARS-CoV-2, and other emerging viruses. Beyond human health, several chalcones have shown potent activity against plant viruses such as tobacco mosaic virus (TMV) and cucumber mosaic virus (CMV), and animal viruses including porcine reproductive and respiratory syndrome virus (PRRSV) and mammalian reovirus (MRV), underscoring their broad antiviral spectrum. These compounds act through multiple mechanisms, including the inhibition of viral enzymes (e.g., proteases, polymerases, and integrases), interference with viral entry and replication, and the modulation of host-related pathways. Recent advances in molecular docking, structure–activity relationship (SAR) studies, and synthetic optimization have further highlighted chalcones as a promising scaffold for antiviral drug discovery. Accordingly, this review summarizes and categorizes antiviral chalcones reported over the last two decades, emphasizing and critically discussing their molecular targets, mechanisms of action, and pharmacological potential as lead compounds. It also provides a comparative perspective on their pharmacological relevance by correlating their activities against standard therapeutic agents and reference inhibitors. Furthermore, the most recurrent viral targets were critically discussed regarding their conservation, expected genetic barriers to resistance, and the global SAR trends identified for the corresponding antiviral chalcones. Finally, in silico ADMET profiling of the most promising naturally occurring chalcones was performed to evaluate their drug-likeness and pharmacokinetic properties, offering guidance for future structural optimization and translational development. Collectively, these findings highlight the chalcone scaffold as a versatile platform for the development of novel antiviral agents targeting diverse viral and host pathways.