Frustrated　Lewis　pair　(FLP)　catalysts　have　attracted　much　recent　interest　because　of　their　exceptional　ability　to　activate　small　molecules　in　homogeneous　catalysis.　In　the　past　ten　years,　this　unique　catalysis　concept　has　been　extended　to　heterogeneous　catalysis,　with　much　success.　Herein,　we　review　the　recent　theoretical　advances　in　understanding　FLP-based　heterogeneous　catalysis　in　several　applications,　including　metal　oxides,　functionalized　surfaces,　and　two-dimensional　materials.　A　better　understanding　of　the　details　of　the　catalytic　mechanism　can　help　in　the　experimental　design　of　novel　heterogeneous　FLP　catalysts.