Little is known about factors controlling the dynamics of aerosol dispersion and deposition in the lung periphery, though this knowledge becomes increasingly important in many fields such as environmental and occupational exposure, diagnostic applications, and therapeutic deliver of drugs via aerosols. For the last several years, we have been studying aerosol behavior in the pulmonary acinus, where the airway structure and the associated fluid mechanics are distinctly different from those in the conducting airways. Our major research efforts have been focused on the basic physics underlying acinar fluid mechanics and particle dynamics, which are likely to be conditioned by the two key geometric factors of acinar airways: structural alveolation and rhythmic expansion and contraction of the alveolar walls. A combination of computational and experimental analyses revealed that due to these unique geometric features acinar flow can be extremely complex despite the low Reynolds number, and can have substantial effects on particle dynamics. In particular, chaotic mixing can occur in the lung periphery. In the course of such a mixing process, the inhaled aerosol particles quickly mix with the residual alveolar gas in a manner that is radically different from the previously considered classical diffusion process. The objective of this paper is to briefly review our current understanding of these processes, to discuss existing deposition models, and to describe our ongoing research efforts toward a basic understanding of aerosol behavior in the pulmonary acinus.