Transparent conducting oxides (TCOs) are a group of materials that are widely used in solar cells and other optoelectronic devices. Recently, Cu-containing p-type TCOs such as MII Cu2 O2 (MIII=Mg, Ca, Sr, Ba) and CuMIII O2 (MIII=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 MII Cu2 O2 , we predict that adding a small amount of Ca into Sr Cu2 O2 can increase the transparency and conductivity. For CuMIII O2, we explained the doping and band gap anomalies in this system and proposed a new approach to search for bipolar dopable wide-gap materials.