Provided are compositions, processes for making, and processes for using triglycerides as plasticizers. Triglyceride plasticizers can be produced by recovery of linear or branched C4 to C10 aldehydes from a hydroformylation product, oxidation to the acid with oxygen and/or air, recovery of the resulting acid, and esterification with glycerol, wherein the total carbon number of the triester groups is from 20 to 25 for greater than or equal to 45 wt % of the plasticizer. Such plasticizers can be phthalate-free and provide outstanding properties including a suitable melting or glass transition or pour point, low volatility, increased compatibility, and excellent low temperature properties in a range of polymeric resins.