EFSA was asked to deliver a scientific opinion on free and esterified 3- and 2-monochloropropane-1,2-diol (MCPD) and glycidyl esters in food. Esters of 3- and 2-MCPD and glycidol are contaminants of processed vegetable oils; free MCPDs are formed in some processed foods. The Panel on Contaminants in the Food Chain (CONTAM Panel) evaluated 7,175 occurrence data. Esters of 3- and 2-MCPD and glycidyl esters were found at the highest levels in palm oil/fat, but most vegetable oil/fats contain substantial quantities. Mean middle bound (MB) dietary exposure values to total 3-MCPD, 2-MCPD and glycidol, respectively, across surveys and age groups in µg/kg body weight (bw) per day were 0.2–1.5, 0.1–0.7 and 0.1–0.9; high exposure (P95) values were 0.3–2.6, 0.2–1.2 and 0.2–2.1. Animal studies show extensive hydrolysis of esterified 3-MCPD and glycidol following oral administration; esterified and free forms were assumed to contribute equally to internal exposures. Nephrotoxicity was consistently observed in rats treated with 3-MCPD. Data on 2-MCPD toxicity were insufficient for dose–response assessments. Chronic treatment with glycidol increased the incidence of tumours in several tissues of rats and mice, likely via a genotoxic mode of action. The Panel selected a BMDL10 value for 3-MCPD of 0.077 mg/kg bw per day for induction of renal tubular hyperplasia in rats and derived a tolerable daily intake (TDI) of 0.8 µg/kg bw per day. The mean exposure to 3-MCPD was above the TDI for ‘Infants’, ‘Toddlers’ and ‘Other children’. For glycidol, the Panel selected a T25 value of 10.2 mg/kg bw per day for neoplastic effects in rats. The margins of exposure (MoEs) were 11,300–102,000 and 4,900–51,000 across surveys and age groups at mean and P95 exposures, respectively. An exposure scenario for infants receiving formula only resulted in MoEs of 5,500 (mean) and 2,100 (P95). MoEs of 25,000 or higher were considered of low health concern.