Vanishing theorems are foundational tools in the Log Minimal Model Program, with the Kawamata-Viehweg Vanishing Theorem being one of the most important. However, these fail in positive characteristics. Fano varieties and their log generalizations are expected to behave better in this setting. In this talk, we prove the Kawamata--Viehweg vanishing theorem for surfaces of del Pezzo type over imperfect fields of characteristic p>5 and discuss consequences to threefold singularities.