Patients with obesity, a reduced exercise capacity, increased cardiac filling pressures and a measured left ventricular ejection fraction in the normal range do not have a homogeneous disorder, but instead, exhibit one of three phenotypes. First, many obese people exhibit sodium retention, plasma volume expansion and cardiac enlargement, and some are likely to have heart failure that is related to hypervolaemia, even though cardiac index and circulating levels of natriuretic peptides are not meaningfully increased. Second, in some middle‐aged men and women (particularly those with minimal co‐morbidities), levels of natriuretic peptides increase markedly and can lower systemic vascular resistance, thus leading to high‐output heart failure (HOHF) and glomerular hyperfiltration. Third, older obese people, particularly women with multiple co‐morbidities, exhibit the syndrome of heart failure with a preserved ejection fraction (HFpEF). Despite degrees of plasma volume expansion similar to HOHF, these patients exhibit only modestly increased ventricular dimensions and circulating levels of natriuretic peptides (despite a high prevalence of atrial fibrillation), and glomerular function is characteristically impaired. A conceptual framework is proposed to distinguish among the three phenotypes seen in obese patients with exercise intolerance, increased ventricular filling pressures and a measured left ventricular ejection fraction in the normal range, since they may respond differently to therapeutic interventions. Efforts are needed to enhance the recognition of heart failure in obese people and to ensure that clinical trials that are designed to study patients with HFpEF actually enrol those who have the disease.