Alphaviruses are typically arthropod-borne, and many are important pathogens such as chikungunya virus. Alphaviruses encode four nonstructural proteins (nsP1-4), initially produced as a polyprotein P1234. nsP4 is the core RNA-dependent RNA polymerase but all four nsPs are required for RNA synthesis. The early replication complex (RC) formed by the polyprotein P123 and nsP4 synthesizes minus RNA strands, and the late RC composed of fully processed nsP1-nsP4 is responsible for the production of genomic and subgenomic plus strands. Different parts of nsP4 recognize the promoters for minus and plus strands but the binding also requires the other nsPs. The alphavirus polymerase has been purified and is capable of de novo RNA synthesis only in the presence of the other nsPs. The purified nsP4 also has terminal adenylyltransferase activity, which may generate the poly(A) tail at the 3' end of the genome. Membrane association of the nsPs is vital for replication, and alphaviruses induce membrane invaginations called spherules, which form a microenvironment for RNA synthesis by concentrating replication components and protecting double-stranded RNA intermediates. The RCs isolated as crude membrane preparations are active in RNA synthesis in vitro, but high-resolution structure of the RC has not been achieved, and thus the arrangement of viral and possible host components remains unknown. For some alphaviruses, Ras-GTPase-activating protein (Src-homology 3 (SH3) domain)-binding proteins (G3BPs) and amphiphysins have been shown to be essential for RNA replication and are present in the RCs. Host factors offer an additional target for antivirals, as only few alphavirus polymerase inhibitors have been described.