Viruses are abiotic obligate parasites utilizing complex mechanisms to hijack cellular machinery and reproduce, causing multiple harmful effects in the process. Viruses represent a growing global health concern; at the time of writing, COVID-19 has killed at least two million people around the world and devastated global economies. Lingering concern regarding the virus' prevalence yet hampers return to normalcy. While catastrophic in and of itself, COVID-19 further heralds in a new era of human-disease interaction characterized by the emergence of novel viruses from natural sources with heretofore unseen frequency. Due to deforestation, population growth, and climate change, we are encountering more viruses that can infect larger groups of people with greater ease and increasingly severe outcomes. The devastation of COVID-19 and forecasts of future human/disease interactions call for a creative reconsideration of global response to infectious disease. There is an urgent need for accessible, cost-effective antiviral (AV) drugs that can be mass-produced and widely distributed to large populations. Development of AV drugs should be informed by a thorough understanding of viral structure and function as well as human biology. To maximize efficacy, minimize cost, and reduce development of drug-resistance, these drugs would ideally operate through a varied set of mechanisms at multiple stages throughout the course of infection. Due to their abundance and diversity, natural compounds are ideal for such comprehensive therapeutic interventions. Promising sources of such drugs are found throughout nature; especially remarkable are the algae, a polyphyletic grouping of phototrophs that produce diverse bioactive compounds. While not much literature has been published on the subject, studies have shown that these compounds exert antiviral effects at different stages of viral pathogenesis. In this review, we follow the course of viral infection in the human body and evaluate the AV effects of algae-derived compounds at each stage. Specifically, we examine the AV activities of algae-derived compounds at the entry of viruses into the body, transport through the body the lymph and blood, infection of target cells, and immune response. We discuss what is known about algae-derived compounds that may interfere with the infection pathways of SARS-CoV-2; and review which algae are promising sources for AV agents or AV precursors that, with further investigation, may yield life-saving drugs due to their diversity of mechanisms and exceptional pharmaceutical potential.