Biological data mainly comprises of Deoxyribonucleic acid (DNA) and protein sequences. These are the biomolecules which are present in all cells of human beings. Due to the self-replicating property of DNA, it is a key constitute of genetic material that exist in all breathingcreatures. This biomolecule (DNA) comprehends the genetic material obligatory for the operational and expansion of all personified lives. To save DNA data of single person we require 10CD-ROMs.Moreover, this size is increasing constantly, and more and more sequences are adding in the public databases. This abundant increase in the sequence data arise challenges in the precise information extraction from this data. Since many data analyzing and visualization tools do not support processing of this huge amount of data. To reduce the size of DNA and protein sequence, many scientists introduced various types of sequence compression algorithms such as compress or gzip, Context Tree Weighting (CTW), Lampel Ziv Welch (LZW), arithmetic coding, run-length encoding and substitution method etc. These techniques have sufficiently contributed to minimizing the volume of the biological datasets. On the other hand, traditional compression techniques are also not much suitable for the compression of these types of sequential data. In this paper, we have explored diverse types of techniques for compression of large amounts of DNA Sequence Data. In this paper, the analysis of techniques reveals that efficient techniques not only reduce the size of the sequence but also avoid any information loss. The review of existing studies also shows that compression of a DNA sequence is significant for understanding the critical characteristics of DNA data in addition to improving storage efficiency and data transmission. In addition, the compression of the protein sequence is a challenge for the research community. The major parameters for evaluation of these compression algorithms include compression ratio, running time complexity etc.