Disclosed are human milk fat (HMF) substitutes, processes for their preparation, uses thereof and fat blends and infants formulae containing them. A fat base composition of the invention comprises a mixture of vegetable-derived triglycerides, with less than 50% of the fatty acid residues bonded at the sn-2 position being saturated; and/or with the amount of saturated fatty acid residues bonded at the sn-2 position of the glycerol backbone less than about 43.5% of the total amount of saturated fatty acid residues. Typically, substantially all of the saturated fatty acids bonded at the sn-2 position of the glycerol backbone are palmitic acid residues. Also disclosed are substitute HMF compositions comprising a blend of at least 25% or at least 30% of the said fat base composition of the invention with up to 75%, or respectively up to 70%, of at least one vegetable oil. Processes for preparing the fat base compositions and blend are also disclosed. Further disclosed are infant formulas comprising the fat base composition or substitute human milk fat composition.