Recent reports on both theoretical simulations and on the physical chemistry basis of spontaneous mirror symmetry breaking (SMSB), that is, asymmetric synthesis in the absence of any chiral polarizations other than those arising from the chiral recognition between enantiomers, strongly suggest that the same nonlinear dynamics acting during the crucial stages of abiotic chemical evolution leading to the formation and selection of instructed polymers and replicators, would have led to the homochirality of instructed polymers. We review, in the first instance, which reaction networks lead to the nonlinear kinetics necessary for SMSB, and the thermodynamic features of the systems where this potentiality may be realized. This could aid not only in the understanding of SMSB, but also the design of reliable scenarios in abiotic evolution where biological homochirality could have taken place. Furthermore, when the emergence of biological chirality is assumed to occur during the stages of chemical evolution leading to the selection of polymeric species, one may hypothesize on a tandem track of the decrease of symmetry order towards biological homochirality, and the transition from the simple chemistry of astrophysical scenarios to the complexity of systems chemistry yielding Darwinian evolution.