Transparent conducting oxides (TCOs) are a group of materials that axe widely used in solar cells and other optoelectronic devices. Recently Cu-containing p-type TCOs such as (MCu2O2)-Cu-II (M-II=Mg, Ca, Sr, Ba) and (CuMO2)-O-III (M-III=Al, Ga, In) have been proposed. Using first-principles band structure methods, we have systematically studied the electronic and optical Properties of these p-type transparent oxides. For (MCu2O2)-Cu-II, we predict that adding a small amount of Ca into SrCu2O2 can increase the transparency and conductivity. For (CuMO2)-O-III, we explained the doping and, band gap anomalies in this system and proposed. a. new approach to search for bipolar dopable wide-gap materials.