Some observers have described the coronavirus pandemic as an 'Anthropocene disease,' thereby highlighting its connection with this new ecological era that is characterised by the considerable pressure human activities are exerting on ecosystems and the consequences on public health, society and the environment. This article focuses on the recent emergence of the 'Planetary Health' paradigm. Launched by the Rockefeller Foundation and the medical journal The Lancet, Planetary Health is one of the most ambitious attempts in recent years to systematize global health in the Anthropocene. While recognising the interest and necessity of reflecting on human health and the health of the planet, this article aims to show, however, that the Planetary Health paradigm is problematic and aporetic for two reasons. First, because it is based on a scientistic and depoliticised conception of the Anthropocene, which obscures capitalism's responsibility for the contemporary global and, especially, ecological crisis. Second, because this conception leads to a promotion of solutions that are essentially based on the financialization and technoscientific management of the living world - precisely the underlying cause of the degradation of ecosystems and living conditions that created the Anthropocene in the first place. A different kind of 'planetary health' remains possible and desirable.