Ambipolar charge carrier transport in Copper phthalocyanine (CuPc) is studied experimentally in field-effect transistors and metal-insulator-semiconductor diodes at various temperatures. The electronic structure and the transport properties of CuPc attached to leads are calculated using density functional theory and scattering theory at the non-equilibrium Greens function level. We discuss, in particular, the electronic structure of CuPc molecules attached to gold chains in different geometries to mimic the different experimental setups. The combined experimental and theoretical analysis explains the dependence of the mobilityand the transmission coefficient on the charge carrier type (electrons or holes) and on the contact geometry. We demonstrate the correspondence between our experimental results on thick films and our theoretical studies of single molecule contacts. Preliminary results for fluorinated CuPc are discussed.