Subcellular organelles are dynamic structures that tune their functions in conjunction with changes to their shapes and compositions. Each organelle has distinct structure-function relationships that change in response to diverse stimuli. Such remodeling events further affect organelle-organelle interaction networks facilitated by membrane contact sites, thereby activating rapid intra- and intercellular communication cascades. As viruses rely on repurposing the host cell machinery during infections, organelle remodeling is a fundamental facet and outcome of all viral infections. Some organelle remodeling events are unique to particular viruses, while others are shared by an array of viruses. Here, we review knowledge derived from this expanding yet still underexplored research area of infection-induced organelle remodeling. We focus on the molecular mechanisms used by viruses to temporally control organelle structure-function relationships. We highlight how organelle remodeling can inhibit host defenses or facilitate specific stages of a virus replication cycle, i.e., entry, replication, assembly, and spread.