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With the exponential growth in the capacity of information generated and the emerging need for data to be stored for prolonged period of time, there emerges a need for a storage medium with high capacity, high storage density, and possibility to withstand extreme environmental conditions. DNA emerges as the prospective medium for data storage with its striking features. Diverse encoding models for reading and writing data onto DNA, codes for encrypting data which addresses issues of error generation, and approaches for developing codons and storage styles have been developed over the recent past. DNA has been identified as a potential medium for secret writing, which achieves the way towards DNA cryptography and stenography. DNA utilized as an organic memory device along with big data storage and analytics in DNA has paved the way towards DNA computing for solving computational problems. This paper critically analyzes the various methods used for encoding and encrypting data onto DNA while identifying the advantages and capability of every scheme to overcome the drawbacks identified priorly. Cryptography and stenography techniques have been analyzed in a critical approach while identifying the limitations of each method. This paper also identifies the advantages and limitations of DNA as a memory device and memory applications.