Organoid technology has transformed experimental virology by offering physiologically relevant 3D human models that bridge the gap between conventional 2D cell cultures and complex in vivo systems. Derived from pluripotent or adult stem cells, organoids self-organize into multicellular structures that recapitulate native tissue architecture and function, enabling more accurate modeling of host–virus interactions and disease mechanisms. This review outlines the evolution and application of organoid-based systems across neural, intestinal, hepatic, pulmonary, and renal tissues for studying a broad range of human viruses that remain a public health burden. These models can reproduce viral tropism, immune signaling, and host variability, offering new molecular insights into infection dynamics. Integration with single-cell transcriptomics, CRISPR editing, and antiviral screening has expanded the translational utility of organoids, establishing them as a powerful platform for antiviral discovery, vaccine testing, and precision medicine.