Endogenous and environmental stressors can damage DNA and RNA to compromise genome and transcriptome stability and integrity in cells, leading to genetic instability and diseases. Recent studies have demonstrated that RNA damage can also modulate genome stability via RNA-templated DNA synthesis, suggesting that it is essential to maintain RNA integrity for the sustainment of genome stability. However, little is known about RNA damage and repair and their roles in modulating genome stability. Current efforts have mainly focused on revealing RNA surveillance pathways that detect and degrade damaged RNA, while the critical role of RNA repair is often overlooked. Due to their abundance and susceptibility to nucleobase damaging agents, it is essential for cells to evolve robust RNA repair mechanisms that can remove RNA damage, maintaining RNA integrity during gene transcription. This is supported by the discovery of the alkylated RNA nucleobase repair enzyme human AlkB homolog 3 that can directly remove the methyl group on damaged RNA nucleobases, predominantly in the nucleus of human cells, thereby restoring the integrity of the damaged RNA nucleobases. This is further supported by the fact that several DNA repair enzymes can also process RNA damage. In this review, we discuss RNA damage and its effects on cellular function, DNA repair, genome instability, and potential RNA damage repair mechanisms. Our review underscores the necessity for future research on RNA damage and repair and their essential roles in modulating genome stability.