Reactive oxygen species (ROS) are harnessed by the cell for signaling at the same time as being detrimental to cellular components such as DNA. The genome and transcriptome contain instructions that can alter cellular processes when oxidized. The guanine (G) heterocycle in the nucleotide pool, DNA, or RNA is the base most prone to oxidation. The oxidatively-derived products of G consistently observed in high yields from hydroxyl radical, carbonate radical, or singlet oxygen oxidations under conditions modeling the cellular reducing environment are discussed. The major G base oxidation products are 8-oxo-7,8-dihydroguanine (OG), 5-carboxamido-5-formamido-2-iminohydantoin (2Ih), spiroiminodihydantoin (Sp), and 5-guanidinohydantoin (Gh). The yields of these products show dependency on the oxidant and the reaction context that includes nucleoside, single-stranded DNA (ssDNA), double-stranded DNA (dsDNA), and G-quadruplex DNA (G4-DNA) structures. Upon formation of these products in cells, they are recognized by the DNA glycosylases in the base excision repair (BER) pathway. This review focuses on initiation of BER by the mammalian Nei-like1-3 (NEIL1-3) glycosylases for removal of 2Ih, Sp, and Gh. The unique ability of the human NEILs to initiate removal of the hydantoins in ssDNA, bulge-DNA, bubble-DNA, dsDNA, and G4-DNA is outlined. Additionally, when Gh exists in a G4 DNA found in a gene promoter, NEIL-mediated repair is modulated by the plasticity of the G4-DNA structure provided by additional G-runs flanking the sequence. On the basis of these observations and cellular studies from the literature, the interplay between DNA oxidation and BER to alter gene expression is discussed.