Transcription presents challenges to genome stability both directly, by altering genome topology and exposing single‐stranded DNA to chemical insults and nucleases, and indirectly by introducing obstacles to the DNA replication machinery. Such obstacles include the RNA polymerase holoenzyme itself, DNA‐bound regulatory factors, G‐quadruplexes and RNA‐DNA hybrid structures known as R‐loops. Here, we review the detrimental impacts of transcription on genome stability in budding yeast, as well as the mitigating effects of transcription‐coupled nucleotide excision repair and of systems that maintain DNA replication fork processivity and integrity. Interactions between DNA replication and transcription have particular potential to induce mutation and structural variation, but we conclude that such interactions must have only minor effects on DNA replication by the replisome with little if any direct mutagenic outcome. However, transcription can significantly impair the fidelity of replication fork rescue mechanisms, particularly Break Induced Replication, which is used to restart collapsed replication forks when other means fail. This leads to de novo mutations, structural variation and extrachromosomal circular DNA formation that contribute to genetic heterogeneity, but only under particular conditions and in particular genetic contexts, ensuring that the bulk of the genome remains extremely stable despite the seemingly frequent interactions between transcription and DNA replication.