Abstract Biospecific molecular recognition in living systems is known to be based on the lock and key principle as proposed by Emil Fischer. Based on this concept, biospecific polymers have been produced synthetically by attaching biospecific ‘keys’ to the polymer chain. We postulate that biospecificity can be achieved by alternative means, namely random substitution of a preformed polymer with suitable chemical groups or random copolymerization of suitable functional monomers. Such polymers, we suggest, will contain arrangements of the chemical functions which mimic natural biospecific sites and the probability of occurrence of such arrangements will depend on the average composition of the polymer. In support of this principle, we have developed several functional random copolymer systems which possess a variety of biological properties depending on the type of chemical function. Examples are: polymers possessing anticoagulant properties similar to those of heparin; polymers which interact specifically with components of the immune system; and polymers which, in contact with cells, affect their growth and metabolism. In the case of statistical copolymers possessing ‘DNA-like’ properties obtained by phosphorylation of hydroxylated polystyrene derivatives, Monte Carlo simulations were used to determine the distribution of phosphodiester (PDE) groups along the chains and to compute the probabilities of occurrence of particular arrangements of PDE found in the ‘DNA-like’ sites. The results showed that these sites are made up of PDE groups separated by distances that closely match those between the same groups along a generatrix of the DNA double-helix cylinder. These findings offer the prospect of manufacturing polymeric biomaterials endowed with biomimetic character. Moreover, they provide the basis for a hypothesis regarding the appearance of biospecificity at the origin of life, suggesting that biospecific structures may have evolved by natural selection from purely random copolymers. It is likely therefore that biospecificity is a continuous function of randomness, arising from purely statistical distributions of reactivity and evolving into precisely defined structures such as those involved in ligand-receptor interactions.