8-oxo-guanine (8OG) is a common base lesion, generated by reactive oxygen species, which has been associated with human diseases such as cancer, aging-related neurodegenerative disorders and atherosclerosis. 8OG is highly mutagenic, due to its dual-coding potential it can pair both with adenine or cytidine. Therefore, it creates a challenge for DNA polymerases striving to correctly replicate and/or repair genomic or mitochondrial DNA. Numerous structural studies provide insights into the mechanistic basis of the specificity of 8OG bypass by DNA polymerases from different families. Here, we focus on how repair polymerases from Family X (Pols β, λ and µ) engage DNA substrates containing the oxidized guanine. We review structures of binary and ternary complexes for the three polymerases, which represent distinct steps in their catalytic cycles—the binding of the DNA substrate and the incoming nucleotide, followed by its insertion and extension. At each of these steps, the polymerase may favor or exclude the correct C or incorrect A, affecting the final outcome, which varies depending on the enzyme.