In 2019, at the World Economic Forum, DNA data storage was indicated as one of the breakthroughs expected to radically impact the global socio-economic order. Indeed, dry DNA is a relatively stable substance and an extremely capacious information carrier. One gram of DNA can hold up to 455 exabytes, provided that one nucleotide encodes two bits of information. In this critical review, the main attention is paid to nucleinography, meaning the conversion of digital data into nucleotide sequences. The evolution and diversity of approaches intended for encoding data with nucleotides are demonstrated. The most noticeable examples of storing minor as well as considerable quantities of non-biological information in DNA are given. Some issues of DNA data storage are also reported.