Copper has several clinically relevant radioisotopes and versatile coordination chemistry, allowing attachment of its radionuclides to biological molecules. This characteristic makes it suitable for applications in molecular imaging or radionuclide targeted therapy. Of particular interest in nuclear medicine today is the theranostic approach. This brief review considers five radionuclides of copper. These are Cu-60, Cu-61, Cu-62, Cu-64, and Cu-67. The first four are positron emitters for imaging, and the last one Cu-67 is a β--emitting radionuclide suitable for targeted therapy. The emphasis here is on theory-aided evaluation of available experimental data with a view to establishing standardised cross-section database for production of the relevant radionuclide in high purity. Evaluated cross section data of the positron emitters have been already extensively reported; so here they are only briefly reviewed. More attention is given to the data of the 68Zn(p,2p)67Cu intermediate energy reaction which is rather commonly used for production of 67Cu.