This chapter provides a review of recently elaborated mathematical models for explaining the salient features of two experimental studies selected for their relevance to the problem of stochastic mirror symmetry breaking and amplification. The first experiment modeled treats the phenomena of mirror symmetry breaking via the autocatalytic crystallization of the glycine and α-amino acid system at the air-water interface. The second experiment deals with the lattice-controlled generation of homochiral oligopeptides, which we model based on a kinetic scheme for copolymerization in a closed reaction system. Since the fundamental paradigm of mutual inhibition lies at the core of both these models, we review how the final asymptotic states in the Frank model depend crucially on whether the system is open or closed, and emphasize the importance of temporary chiral excursions, which can and do arise in more complex reaction schemes during their approach to chemical equilibrium in closed systems.