Research coupling human nutrition and sustainability concerns is a rapidly developing field, which is essential to guide governments’ policies. This critical and comprehensive review analyzes indicators and approaches to “sustainable healthy diets” published in the literature since this discipline’s emergence a few years ago, identifying robust gauges and highlighting the flaws of the most commonly used models. The reviewed studies largely focus on one or two domains such as greenhouse gas emissions or water use, while overlooking potential impact shifts to other sectors or resources. The present study covers a comprehensive set of indicators from the health, environmental and socio-economic viewpoints. This assessment concludes that in order to identify the best food option in sustainability assessments and nutrition analysis of diets, some aspects such as the classification and disaggregation of food groups, the impacts of the rates of local food consumption and seasonality, preservation methods, agrobiodiversity and organic food and different production systems, together with consequences for low-income countries, require further analysis and consideration.