Abstract-much of our scientific, technological, and economic future depends on the availability of an ever-increasing supply of computational power. However, the increasing demand for such power has pushed electronic technology to the limit of physical feasibility and has raised the concern that this technology may not be able to sustain our growth in the near future. It became important to consider an alternative means of achieving computational power. In this regard, DNA computing was introduced based on the usage of DNA and molecular biology hardware instead of the typical silicon based technology. The molecular computers could take advantage of DNA's physical properties to store information and perform calculations. These include extremely dense information storage, enormous parallelism and extraordinary energy efficiency. One of the main advantages that DNA computations would add to computation is its self -parallel processing while most of the electronic computers now use linear processing. In this paper, the DNA computation is reviewed and its state of the art challenges and applications are presented. Some of these applications are those require fast processing, at which DNA computers would be able to solve the hardest problems faster than the traditional ones. For example, 10 trillion DNA molecules can fit in one cubic centimeter that would result in a computer that holds 10 terabytes of data. Moreover, this work focuses on whether a large scale molecular computer can be built.