Since conventional thermal processing can have detrimental consequences on aroma compounds, non-thermal technologies such as high hydrostatic pressure (HHP) have been explored. HHP may alter the weak chemical bonds of enzymes. These changes can modify the secondary, tertiary, and quaternary structures of key enzymes in the production of aroma compounds. This can result in either an increase or decrease in their content, along with reactions or physical processes associated with a reduction of molecular volume. This article provides a comprehensive review of HHP treatment’s effects on the content of lipid-derived aroma compounds, aldehydes, alcohols, ketones, esters, lactones, terpenes, and phenols, on various food matrices of vegetable and animal origin. The content of aldehydes and ketones in food samples increased when subjected to HHP, while the content of alcohols and phenols decreased, probably due to oxidative processes. Both ester and lactone concentrations appeared to decline due to hydrolysis reactions. There is no clear tendency regarding terpenes concentration when subjected to HHP treatments. Because of the various effects of HHP on aroma compounds, an area of opportunity arises to carry out future studies that allow optimizing and controlling the effect.