Genome instability is an enabling characteristic of cancer, essential for cancer cell evolution. Hotspots of genome instability, from small-scale point mutations to large-scale structural variants, are associated with sequences that potentially form non-B DNA structures. G-quadruplex (G4) forming motifs are enriched at structural variant endpoints in cancer genomes. Chronic inflammation is a physiological state underlying cancer development, and oxidative DNA damage is commonly invoked to explain how inflammation promotes genome instability. We summarize where G4s and oxidative stress overlap, with a focus on DNA replication. Guanine has low ionization potential, making G4s vulnerable to oxidative damage. Impacts to G4 structure are dependent upon lesion type, location, and G4 conformation. Occasionally, G4s pose a challenge to replicative DNA polymerases, requiring specialized DNA polymerases to maintain genome stability. Therefore, chronic inflammation creates a dual challenge for DNA polymerases to maintain genome stability: faithful G4 synthesis and bypassing unrepaired oxidative lesions. Inflammation is also accompanied by global transcriptome changes that may impact mutagenesis. Several studies suggest a regulatory role for G4s within cancer- and inflammatory-related gene promoters. We discuss the extent to which inflammation could influence gene regulation by G4s, thereby impacting genome instability, and highlight key areas for new investigation.