Sustainability in food system is a grand challenge in our time. Delivering food and nutrition in a secure and sustainable manner across the eco-environmental and social pillars of sustainability is by far an ambitious goal. Understanding the developments in sustainable food system is crucial to undertake informed decisions. To this end, this paper aims to provide a comprehensive review of sustainability in the food industries covering sustainability's three dimensions: environmental, socio-economic, and eco-environmental aspects. A four-method approach has been used to assess the papers found on the Scopus database, limiting the review for the past ten years of research. For each dimension, the most used assessment tools used by researchers are mentioned under each dimension section. Besides variable selection approaches covered in the research review, modeling and optimization techniques have been listed.