Obesity‐related respiratory failure is increasingly common but remains under‐diagnosed and under‐treated. There are several clinical phenotypes reported, including severe obstructive sleep apnoea (OSA), isolated nocturnal hypoventilation with or without severe OSA and OSA complicating chronic obstructive pulmonary disease (COPD). The presence of hypercapnic respiratory failure is associated with poor clinical outcomes in each of these groups. While weight loss is a core aim of management, this is often unachievable, and treatment of sleep‐disordered breathing with positive airway pressure (PAP) therapy is the mainstay of clinical practice. Although there are few long‐term clinical efficacy trials, the lack of equipoise would prevent the utilization of an untreated control group. The current data support the use of PAP therapy to improve respiratory failure and is associated with improvements in health‐related quality of life, reduced healthcare utilization and reduced mortality. Both continuous PAP (CPAP) and non‐invasive ventilation (NIV) appear safe and effective in patients with obesity‐related respiratory failure and OSA, with or without COPD, and the current evidence would not support a single therapy choice in all patients. There are no studies of CPAP in patients with isolated nocturnal hypoventilation, and NIV would be the current recommendation in this patient group. Whichever starting therapy is used, titration should be performed to correct sleep‐disordered breathing and reverse chronic respiratory failure, with consideration of step‐down of the treatment based on a clinical re‐evaluation. In contrast, failure to reach physiological and clinical treatment targets should lead to the consideration of treatment escalation.