The development of agents capable of cleaving RNA and DNA has attracted considerable attention from researchers in the last few years, because of the immediate and very important applications they can find in the emerging fields of biotechnology and pharmacology. There are essentially two classes of these agents - nucleases that occur naturally inside cells and synthetically produced artificial nucleases. The first class includes protein enzyme nucle- ases and catalytic RNA structured ribozymes that perform cleavage of the phosphodiester bonds in nucleic acids according to a hydrolytic pathway in the course of different biochemical processes in the cell. A different pathway is used by some antibiotics which cleave DNA via redox-based mechanisms resulting in oxidative damage of nucleotide units and breakage of the DNA backbone. The above molecules are indispensable tools for manipulating nucleic acids and processing RNA; DNA-cleaving antibiotics and cytotoxic ribonucleases have demonstrated utility as chemotherapeutic agents. The second class, artificial nucleases, are rationally designed to imitate the active centers of natural enzymes by simple structures possessing minimal sets of the most important characteristics that are essential for catalysis. A dif- ferent approach, in vitro selection, was also used to create artificial RNA and DNA enzymes capable of cleaving RNA. Being less efficient and specific as compared to the natural enzymes, the primitive mimics are smaller and robust and can function in a broad range of conditions.