Charge carrier trapping centers have been studied in molybdates CaMoO4, SrMoO4 and PbMoO4 with the scheelite crystal structure as well as in ZnMoO4, which crystallize in a-ZnMoO4 structural type. The trap parameters such as activation energies and frequency factors have been determined. It is shown for the first time that both electrons and holes are trapped by the elements of regular crystal structure in ZnMoO4. The effect of the charge carrier trapping on luminescence properties is demonstrated. Potential influence of the traps on the scintillation process is discussed.