Biocomputers can be an alternative for traditional "silicon-based" computers, which continuous development may be limited due to further miniaturization (imposed by the Heisenberg Uncertainty Principle) and increasing the amount of information between the central processing unit and the main memory (von Neuman bottleneck). The idea of DNA computing came true for the first time in 1994, when Adleman solved the Hamiltonian Path Problem using short DNA oligomers and DNA ligase. In the early 2000s a series of biocomputer models was presented with a seminal work of Shapiro and his colleguas who presented molecular 2 state finite automaton, in which the restriction enzyme, FokI, constituted hardware and short DNA oligomers were software as well as input/output signals. DNA molecules provided also energy for this machine. DNA computing can be exploited in many applications, from study on the gene expression pattern to diagnosis and therapy of cancer. The idea of DNA computing is still in progress in research both in vitro and in vivo and at least promising results of these research allow to have a hope for a breakthrough in the computer science.