The aim of the paper is to make a review of DNA computing achievements on current stage, especially on new approaches or methods contributing to solve either theoretical or application problems. Starting with the NP-problem that Adleman solved by means of wet DNA experiment in 1994, DNA becomes one of the most appropri- ate alternatives to overcome the silicon computer limitations. Today, many researchers concentrate on this research subject either to improve available methods used in DNA computing itself or to suggest a new way to solve engineering or application problems with a DNA computing approach. This paper gives an overview of research achievements in DNA computing and touches on the achievements of improving methods employed in DNA computing as well as in solving application problems. At the end of discussion we address several challenges that DNA computing are facing in the society.