The first step in mathematically modeling the mechanics of respiratory deposition of particles is to estimate the ability of a particle to enter the head, either through the mouth or nose. Models of the biological effects from inhaled particles are commonly, albeit incorrectly, simplified by making an assumption that the only particles of concern are those that can readily penetrate to the pulmonary region of the lung: typically particles less than 5microm in aerodynamic diameter. Inhalability for particles of this size is effectively 100%, so there is little need to develop a mathematical representation of the phenomenon. However, chemical irritants, biological agents, or radioactive material, in the form of large particles or droplets, can cause adverse biological responses by simply being taken into the head and depositing in the extrathoracic area. As a result, it is important to understand the inhalability of both small and large particles. The concept of particle inhalability received little consideration until the 1970s; since then it has been the subject of many experiments with a fairly wide disparity of results, in part due to the variety of dependent variables and the difficulty in adequate measurement methods. This article describes the currently utilized models of inhalability, recommends specific methods for implementing inhalability into mathematical models of respiratory deposition, and identifies outstanding issues and limitations. In this article, we describe inhalability as it applies to particulate matter and liquid droplets; modeling the inhalability of fibers is a work in progress and is not addressed.