Acute respiratory failure (ARF) is a life-threatening condition that occurs when the respiratory system fails to provide sufficient oxygen to the blood. Patients with ARF consume a disproportionate amount of hospital resources, mortality rates are high, and survivors report low health-related quality of life. Treatment is primarily based on providing external respiratory support, starting with supplementary oxygen delivered by low- or high-flow nasal cannula therapy, which may be escalated to non-invasive ventilation (NIV), and ultimately to endotracheal intubation and invasive mechanical ventilation in the intensive care unit (ICU). Each step of this treatment staircase involves the use of significantly greater hospital resources, and requires clinicians to make critical decisions in a time-pressured and resource-limited environment, with access to incomplete information about the state of the patient. Digital Twins of patients based on mechanistic computational models that reflect the underlying disease pathophysiology can provide insight into the effects of different ventilation strategies in different patients, facilitating stratification of patients and personalisation of treatments, and opening up the possibility of designing in silico clinical trials of different interventions. This potential is particularly relevant in the context of respiratory support in intensive care medicine, where research into personalised ventilation strategies has made limited progress, and randomised controlled trials are extremely costly and difficult to execute. In parallel with this approach, the development of data-driven Digital Twins using machine learning and other AI methodologies could provide real-time decision support tools to assist clinicians in deciding how best to treat individual patients. In this talk, I will discuss some recent and new results from our group illustrating how digital twins could be used to improve patient outcomes and reduce the costs associated with treating acute respiratory failure.