Triacylglycerols (TGs) are principal components of vegetable oils and animal fats. Natural TGs form extremely complex mixtures composed of tens or hundreds of molecular species. HPLC/MS suits well for their analyses, but manual data processing is laborious and time-consuming. Specialized software algorithms are needed to accelerate the interpretation process. Here we present software named TriglyAPCI for interpreting APCI, APPI, or ESI MS/MS spectra of TGs. The chapter shows how to build and use the software, what are its advantages and limitations. The algorithm uses diacylglycerol fragments and molecular adducts for determining TG structure. Each ion in a spectrum is tested whether it might be a fragment or a molecular adduct. If so, the number of carbons and double bonds is assigned to it. The relations among the ions are searched and possible structures are suggested. TriglyAPCI allows interpreting spectra of single compounds, mixtures, or incomplete spectra lacking one of the diagnostic ions. The fragment intensities are used to distinguish regioisomers. An efficient chromatographic separation of TGs is shown to be crucial for correct spectra interpretation and avoiding false positive results. TriglyAPCI performance is demonstrated for HPLC/APCI-MS data of TGs isolated from bumblebee Bombus rupestris .