A key challenge for the sustainability of food systems is the question of how to use food that ends up uneaten. One popular guideline for this purpose in OECD countries has been waste hierarchies, such as the European waste hierarchy and the 3R approach to "reduce, reuse, recycle", applied to food. Yet despite their popularity, waste hierarchies applied to food are not systematically being implemented. Moreover, a systematic assessment of the effectiveness of the food waste hierarchy in achieving more efficient resource use and reducing environmental impacts is currently not available. We present here a systematic literature review to fill this gap. Our interdisciplinary review has revealed four core insights. First, the waste hierarchy applied to food works well with greenhouse gas emissions but needs adjustments for other environmental impacts. Second, assessments of food waste prevention, although confirmed as the option of highest priority, are under-represented in the reviewed literature. Third, an emerging body of research includes decision criteria for food waste management related to the characteristics of food. Fourth, there are numerous barriers to prioritization of the prevention of food waste. We demonstrate a limited potential of the current "waste approach to food waste" to reduce environmental impacts occurring from food waste. Implications for research, for example concerning the lagging behind in food prevention, provide an opportunity for research and policy to change the focus towards a "food approach to food waste".