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Transforming food systems is essential for global sustainability and requires understanding from both socioeconomic and physical dimensions. However, sustainable food systems literature is largely dominated by socioeconomic dimension, while physical understanding of food systems remains limited. Such physical characterisation is often done using material flow analysis (MFA) to explore and quantify flows from farm to fork. This quantification translates food system dynamics into comparable and transparent metrics, making MFA a crucial tool in driving an efficient transformation. Here, using a critical literature review, we analysed 127 agrifood MFA studies on their systems, data, and indicators. We characterized food supply chain into five stages (primary production, processing and manufacturing, trade, distribution and retailing, and public and household consumption) and found very few covered all stages (16 studies). Among all stages, primary production was the most studied (99 studies), while distribution and retailing was the least studied (33 studies). Existing studies covered 12 food categories, primarily focusing on cereals (52 %), vegetables (46 %), and meats (43 %), with less attention on dairy products (34 %). Only 34 studies have a single food category resolution, while most aggregated multiple categories together. We found that over half of agrifood MFAs used data only from secondary sources (e.g., statistics), whereas less than 20 % used exclusively primary data. Agrifood MFAs commonly used indicators of substance, food, and bio-nutrient to quantify biomass associated flows, informing key food systems issues like nutrient circularity and waste management. Accordingly, we call for research on full chain MFAs, single food category analyses, and the use of more targeted datasets. • We reviewed 127 agrifood material flow analysis studies on system, data, and indicator. • Full chain MFAs are rare with trade and distribution and retailing stages most often overlooked. • Food categories were studied widely but mostly in an aggregation manner. • The use of secondary data far exceeded primary data. • Most studies focused on flows of substance, food, and bio-nutrient within food systems.