Despite culturing the fastest-growing animal in animal husbandry, fish farmers are often adversely economically affected by pathogenic disease outbreaks across the world. Although there are available solutions such as the application of antibiotics to mitigate this phenomenon, the excessive and injudicious use of antibiotics has brought with it major concerns to the community at large, mainly due to the rapid development of resistant bacteria. At present, the use of natural compounds such as phytocompounds that can be an alternative to antibiotics is being explored to address the issue of antimicrobial resistance (AMR). These phytocompounds are bioactive agents that can be found in many species of plants and hold much potential. In this review, we will discuss phytocompounds extracted from plants that have been evidenced to contain antimicrobial, antifungal, antiviral and antiparasitic activities. Further, it has also been found that compounds such as terpenes, phenolics, saponins and alkaloids can be beneficial to the aquaculture industry when applied. This review will focus mainly on compounds that have been identified between 2000 and 2021. It is hoped this review will shed light on promising phytocompounds that can potentially and effectively mitigate AMR.