A substantial fraction of the total ultrafine particulate mass is comprised of organic compounds. Of this fraction, a significant subfraction is secondary organic aerosol (SOA), meaning that the compounds are a by-product of chemistry in the atmosphere. However, our understanding of the kinetics and mechanisms leading to and following SOA formation is in its infancy. We lack a clear description of critical phenomena; we often don't know the key, rate limiting steps in SOA formation mechanisms. We know almost nothing about aerosol yields past the first generation of oxidation products. Most importantly, we know very little about the derivatives in these mechanisms; we do not understand how changing conditions, be they precursor levels, oxidant concentrations, co-reagent concentrations (i.e., the VOC/NOx ratio) or temperature will influence the yields of SOA. In this paper we explore the connections between fundamental details of physical chemistry and the multitude of steps associated with SOA formation, including the initial gas-phase reaction mechanisms leading to condensible products, the phase partitioning itself, and the continued oxidation of the condensed-phase organic products. We show that SOA yields in the alpha-pinene + ozone are highly sensitive to NOx, and that SOA yields from beta-caryophylene + ozone appear to increase with continued ozone exposure, even as aerosol hygroscopicity increases as well. We suggest that SOA yields are likely to increase substantially through several generations of oxidative processing of the semi-volatile products.