64Cu (Iβ+ = 17%, Iβ− = 39%, IEC = 43%) is an important emerging biomedical radionuclide that is suitable for labelling a wide range of radiopharmaceuticals for PET imaging, as well as systemic or local radioimmunotherapy of tumours. Its positron energy spectrum is comparable with that of 18F, allowing high spatial resolution in PET imaging. Its intermediate half-life (12.7 h) permits PET evaluation of slow biochemical pathways, such as protein and peptide interactions with cellular targets, and distribution to satellite imaging and therapy centres. The optimum production route for radiochemically-pure, carrier-free 64Cu is via the reaction 64Ni(p,n) at 12 → 9 MeV followed by anion exchange chromatography. Biomedical applications follow three principal strategies: (i) direct application of 64Cu as a biological tracer, (ii) complexing with redox sensitive ligands (e.g. bisthiosemicarbazones) that release 64Cu upon reduction in hypoxic cells, and (iii) coordination with bifunctional ligands (e.g. tetraaza macrocycles) that covalently bond to intact antibodies, antibody fragments, peptides, peptide analogues or shell cross-linked nanoparticles for targeting receptors expressed by tumours.