Abstract: In recent years there has been a lot of progress on understanding the derived category surfaces of general type with geometric genus zero. Such surfaces have many features in common with del Pezzo surfaces. The first exceptional collection of maximal length on a surface of general type was constructed by Böhning--Graf von Bothmer--Sosna, and this lead to the discovery of so-called "phantom categories". That is, categories which leave (almost) no trace in K-theory or in homology. I will review several famous constructions of surfaces of general type with geometric genus zero, their connection with del Pezzo surfaces, and exhibit several exceptional collections and associated phantoms. Time permitting, I will discuss new questions arising from existence of phantoms.