Although polyamines (PA) belong to relatively simple aliphatic substances, their role in life processes of animals and plants is of key importance [1–5]. The group of the most important amines, called biogenic ones includes: Spermine (Spm): H2N(CH2)3NH(CH2)4NH(CH2)3NH2 Spermidine (Spd): H2N(CH2)3NH(CH2)4NH2 Putrescine (Put): H2N(CH2)4NH2. Of secondary importance are homologues of biogenic amines, occurring in lower contents in living organisms [2, 6–8]: 1,3-diaminopropan: H2N(CH2)3NH2 Cadaverine: H2N(CH2)5NH2 Homospermidine: H2N(CH2)4NH(CH2)4NH2 Norspermine (3,3,3-tet): H2N(CH2)3NH(CH2)3NH(CH2)3NH2 Thermospermine: H2N(CH2)3NH(CH2)4NH(CH2)4NH2 Caldopentamine: H2N(CH2)3NH(CH2)3NH(CH2)3NH(CH2)3NH2. The first polyamine discovered in a living organism was tetramine, a spermine crystallised out of sperm in 1678 by Van Leewenkeuk . Putrescine was discovered in the end of the 19th century in microbes and then triamine: spermidine was discovered in the beginning of the 20th century . Later studies have shown that in animal cells spermidine and spermine occur at elevated levels, while in prokaryotes spermidine and putrescine contents are dominant. Putrescine, spermidine, 1,3-diaminopropan, homospermidine, norspermidine, and norspermine have been found in many gramnegative bacteria and algae [7, 10, 11]. Total concentration of PA in living organisms is on the order of millimols, however, the concentration of free polyamines is much lower. A low level of free amines follows from the fact that they are involved in noncovalent interactions with biomolecules occurring in living organisms such as nucleic acids, proteins, or phospholipids. High concentrations of non-bonded polyamines have been detected first of all in young molecules in the process of growth, in particular in rapidly proliferating cancer cells [6, 12]. Elevated levels of free polyamines have been observed, e.g. in breast, colon, lung, prostate, and skin tumours, accompanied by changed levels of enzymes responsible for biosynthesis and catabolism of polyamines. Because of the increased level of free polyamines and a tendency of their interaction with nucleic acids and other bioligands, these compounds have become objects of intense study [1, 13–19]. There is no doubt that the regulation of biosynthesis of polyamines and catabolism is one of the most important pathways in the search strategy for chemoprevention and chemotherapeutic drugs [14, 15, 20–36]. The present state of knowledge of these processes, their significance in biological systems, and their application in medicine are presented in subsequent sections of this chapter.