Given that breathing is one of the most fundamental physiological functions, there is an urgent need to broaden our understanding of the fluid dynamics that governs it. There would be many benefits from doing so, including a better assessment of respiratory health, a basis for more precise delivery of pharmaceutical drugs for treatment, and the understanding and potential minimization of respiratory infection transmission. We review the physics of particle generation in the respiratory tract, the fate of these particles in the air on exhalation and the physics of particle inhalation. The main focus is on evidence from experimental studies. We conclude that although there is qualitative understanding of the generation of particles in the respiratory tract, a basic quantitative knowledge of the characteristics of the particles emitted during respiratory activities and their fate after emission, and a theoretical understanding of particle deposition during inhalation, nevertheless the general understanding of the entire process is rudimentary, and many open questions remain.