Described here are devices for altering the flow of air in a respiratory cavity such as the mouth and nostrils of the nose. These methods and devices may be useful for affecting a physiologic benefit in patients suffering from a variety of medical diseases, particularly those that may benefit from “pursed-lip” breathing and non-invasive ventilation, such as COPD, heart failure, sleep apnea, and other medical disorders. The devices are typically removable devices that may be placed over or in a respiratory cavity to increase resistance to airflow within the respiratory cavity. Resistance to expiration may be selectively increased relative to inspiration. Removable oral and removable nasal devices are described. Oral and nasal devices that filter inhaled airflow of debris and allergens are also provided. A nasal device that increases patency of the nares is also provided.