Molecular imaging is an important scientific discipline that plays a major role in clinical medicine and pharmaceutical development. While several imaging modalities including X-ray computed tomography (CT) and magnetic resonance imaging (MRI) generate high-resolution anatomical images, positron emission tomography (PET) and single photon emission computed tomography (SPECT) offer insight into the physiological processes that occur within a living organism. Of these two nuclear medicine imaging techniques, PET has advantages with respect to sensitivity and resolution, and this has led to the production and development of many positron emitting radionuclides that include non-traditional radionuclides of the transition metals. Copper-64 (t(1/2) = 12.7 h, beta(+): 17.4%, E(beta+max) = 656 keV; beta(-): 39%, E(beta-max) = 573 keV) has emerged as an important positron emitting radionuclide that has the potential for use in diagnostic imaging and radiotherapy. However, (64)Cu must be delivered to the living system as a stable complex that is attached to a biological targeting molecule for effective imaging and therapy. Therefore, significant research has been devoted to the development of ligands that can stably chelate (64)Cu. This review discusses the necessary characteristics of an effective (64)Cu chelator, while highlighting the development and evaluation of (64)Cu-complexes attached to biologically-targeted ligands.