Alphavirus non-structural proteins 1–4 (nsP1, nsP2, nsP3, and nsP4) are known to be crucial for alphavirus RNA replication and translation. To date, nsP3 has been demonstrated to mediate many virus–host protein–protein interactions in several fundamental alphavirus mechanisms, particularly during the early stages of replication. However, the molecular pathways and proteins networks underlying these mechanisms remain poorly described. This is due to the low genetic sequence homology of the nsP3 protein among the alphavirus species, especially at its 3′ C-terminal domain, the hypervariable domain (HVD). Moreover, the nsP3 HVD is almost or completely intrinsically disordered and has a poor ability to form secondary structures. Evolution in the nsP3 HVD region allows the alphavirus to adapt to vertebrate and insect hosts. This review focuses on the putative roles and functions of indel, repetition, and duplication events that have occurred in the alphavirus nsP3 HVD, including characterization of the differences and their implications for specificity in the context of virus–host interactions in fundamental alphavirus mechanisms, which have thus directly facilitated the evolution, adaptation, viability, and re-emergence of these viruses.