The emergence of the homochiral proteins and nucleic acids, composed from residues of L-amino acids and D-sugars respectively, from the achiral prebiotic world still provides an unsolved conundrum in the field of the origin of life. This mist results from the fundamental symmetry rules as defined, at the end of the nineteenth century, by the Curie principle [1], which states that, '' . . . a physical event cannot have a symmetry lower than that of the event that caused it.''There are two classes of asymmetric transformation, which are in keeping with this symmetry rule. In the first class, chiral reactants are converted, via chemical reactions, into chiral products; in the second class, ''mirror-symmetry'' can be broken spontaneously in either a single or a small number of chemical reactions. In a large number of related independent events, however, the system will preserve its initial nonchiral symmetry. Such class of stochastic asymmetric transformations might have been relevant to chiro-biogenesis, provided the scenario can be accepted that life started in a small number of locations, and that the handedness generated by chance has been amplified and propagated during a competition with heterochiral architectures, such that one of the homochiral architectures has tripped and the other has won the rivalry [2][3][4][5].In this chapter, the second class of stochastic asymmetric synthesis of polymers -referred to as ''absolute'' asymmetric synthesis -and which has been materialized in laboratory experiments, is described. Several successful systems of ''mirror-symmetry breaking'' have been shown to comprise the following steps: spontaneous self-assembly of molecules into crystalline-like supramolecular architectures that create a local homochiral molecular environment exerting asymmetric induction in the ensuing propagation of the polymerization reaction. Farina [6] coined the term ''through-space'' asymmetric transformations in order to distinguish them from the common ''through-bond'' reactions.Here, attention is confined especially to the asymmetric transformations of achiral monomers within crystalline or quasi-crystalline architectures. In particular, the early studies of asymmetric polymerizations performed within enantiomorphous