The chemistry of abiotic nucleotide synthesis of RNA and DNA in the context of their prebiotic origins on early earth is a continuing challenge. How did (or how can) the nucleotides form and assemble from the small molecule inventories and under conditions that prevailed on early earth 3.5-4 billion years ago? This review provides a background and up-to-date progress that will allow the reader to judge where the field stands currently and what remains to be achieved. We start with a brief primer on the biological synthesis of nucleotides, followed by an extensive focus on the prebiotic formation of the components of nucleotides-either via the synthesis of ribose and the canonical nucleobases and then joining them together or by building both the conjoined sugar and nucleobase, part-by-part-toward the ultimate goal of forming RNA and DNA by polymerization. The review will emphasize that there are-and will continue to be-many more questions than answers from the synthetic, mechanistic, and analytical perspectives. We wrap up the review with a cautionary note in this context about coming to conclusions as to whether the problem of chemistry of prebiotic nucleotide synthesis has been solved.