Modern applications of scintillators in medical imaging of human body (Positron Emission Tomography -PET scanning, γ-cameras and other X-ray tomographies) require lmproved or even quite new scinntillators which should be characterized by (i) fast response, (ii) high density and (iii) high light yleld. At present time new scintillating crystals are investigated, mainly those having perovskite lattice structure of the formula RE3+ AlO 3 :Ce where RE3 + = Y3 +, Gd3+ and Lu3 +. Here, we will present the newest data with summarising properties of these types of scintillators including the mixed ones. Energy transfer processes between Ce 3 + main centres and Ce3+ mul -t i s i t e s a r e d i s c u s s e d t o g e t h e r w i t h t h e i r m e c h a n i s m s i n c l u d i n g p r o c e s s e s b etween Ce3 + and Gd3 + ions. Finally, the characteristic properties of scintillating crystals based on perovskite structure are reviewed.