The dynamics of respiratory airflows and the associated transport mechanisms of inhaled aerosols characteristic of the deep regions of the lungs are of broad interest in assessing both respiratory health risks and inhalation therapy outcomes. In the present review, we present a comprehensive discussion of our current understanding of airflow and aerosol transport phenomena that take place within the unique and complex anatomical environment of the deep lungs, characterized by submillimeter 3D alveolated airspaces and nominally slow resident airflows, known as low-Reynolds-number flows. We exemplify the advances brought forward by experimental efforts, in conjunction with numerical simulations, to revisit past mechanistic theories of respiratory airflow and particle transport in the distal acinar regions. Most significantly, we highlight how microfluidic-based platforms spanning the past decade have accelerated opportunities to deliver anatomically inspired in vitro solutions that capture with sufficient realism and accuracy the leading mechanisms governing both respiratory airflow and aerosol transport at true scale. Despite ongoing challenges and limitations with microfabrication techniques, the efforts witnessed in recent years have provided previously unattainable in vitro quantifications on the local transport properties in the deep pulmonary acinar airways. These may ultimately provide new opportunities to explore improved strategies of inhaled drug delivery to the deep acinar regions by investigating further the mechanistic interactions between airborne particulate carriers and respiratory airflows at the pulmonary microscales.