Next Generation Sequencing (NGS) raises opportunities to the computational field for fast and accurate methods for the various challenges associated with NGS data. NGS technology generates a large set of short reads of size 50 to 400 base pairs as a result of biological experiments done on the samples taken from species. Such raw reads are not directly ready for doing most of the analysis or comparative studies to figure out medical related solutions. Hence, the reads have to be assembled to form a complete genome sequence. During the assembly process, there is a high chance of erroneous positioning. Some strategy has to be applied to correct such errors. Once the error-free sequence data is prepared, it is ready for further analysis. The analysis may assist in identifying disease and its cause, similarity check, genetic issue, etc. All of these processes involve data of huge size (in terms of millions per day). To improve the performance of the algorithms working on such vast amount of data, the latest technologies such as Big Data and Cloud Computing can be incorporated. Here, in this paper the evolution of the algorithms for NGS data alignment and the role of Big Data and Cloud Computing technologies are discussed.