DNA cryptography is a new born cryptographic field emerged with the research of DNA computing, in which DNA is used as information carrier and the modern biological technology is used as implementation tool. The vast parallelism and extraordinary information density inherent in DNA molecules are explored for cryptographic purposes such as encryption, authentication, signature, and so on. In this paper, we briefly introduce the biological background of DNA cryptography and the principle of DNA computing, summarize the progress of DNA cryptographic research and several key problems, discuss the trend of DNA cryptography, and compare the status, security and application fields of DNA cryptography with those of traditional cryptography and quantum cryptography. It is pointed out that all the three kinds of cryptography have their own advantages and disadvantages and complement each other in future practical application. The current main difficulties of DNA cryptography are the absence of effective secure theory and simple realizable method. The main goal of the research of DNA cryptography is exploring characteristics of DNA molecule and reaction, establishing corresponding theories, discovering possible development directions, searching for simple methods of realizing DNA cryptography, and laying the basis for future development.