Vertical farming (VF), the cultivation of crops in enclosed and sunless environments, is touted as a solution to global challenges like population growth, urbanization, and climate change, thanks to land conservation, sustainability, reduced water usage, enhanced food safety, and shorter supply chains. This review critically analyses the sustainability claims of VF by particularly focusing on crop energy budgets and productivity. It makes evident that staple crops, vital for calorie intake, cannot be economically grown in VF. Nonetheless, leafy vegetables can and are grown in VF. Based on existing literature, we quantify VF's annual production potential and its associated electricity consumption. We use figures about electricity production to demonstrate that it is doubtful that urban VF production is more climate-smart than transport from far away. It is indeed wishful thinking that there is no environmental cost to getting rid of (free and non-polluting) sun light, even for the very best lighting fixtures. Even in a future world of green (but not unlimited) electricity, there will be a need for balancing grid usage, which does not fit well with the electricity craving of VFs. While VF significantly reduces water use and avoids chemical emissions, these benefits can also be attained in greenhouses, and they often fail to outweigh the environmental impact of electricity consumption. VF may have potential for niche crop production, or be employed for other practical reasons. However, our review challenges the claim that VF production is inherently more environmentally friendly than conventional agriculture.