Overweight and obesity have reached epidemic proportions in the USA and most of the rest of the world. Particularly concerning is the very high prevalence of class III obesity (BMI ≥40 kg/m(2)), which has reached ∼3% in the USA. In the past few years, controversy has surrounded the idea that some individuals with obesity can be considered healthy with regards to their metabolic and cardiorespiratory fitness, which has been termed the 'obesity paradox'. These controversies are reviewed in detail here, including discussion of the very favourable prognosis in patients with obesity who have no notable metabolic abnormalities and who have preserved fitness. The article also discusses the suggestion that greater emphasis should be placed on improving fitness rather than weight loss per se in the primary and secondary prevention of cardiovascular diseases, at least in patients with overweight and class I obesity (BMI 30-35 kg/m(2)).