During the carcinogenesis process, tumour cells often have a more rapid proliferation potential than cells that participate in blood capillary formation by neoangiogenesis. As a consequence of the poorly organized vasculature of various solid tumours, a limited oxygen delivery is observed. This hypoxic mechanism frequently occurs in solid cancers and can lead to therapeutic resistance. The present selected literature review is focused on the comparison of two positron emitting radiopharmaceuticals agents, which are currently leaders in tumour hypoxia imaging by PET. {18F}-fluoromisonidazole (=FMISO) is most commonly used as an investigational PET agent with an investigational new drug exemption from the FDA, while {64Cu}-diacetyl-bis(N4-methylthiosemicarbazone) (64Cu-ATSM) has been presented as an alternative radiopharmaceutical not yet readily available. The comparison of these two radiopharmaceutical agents is particularly focused on isotope properties, radiopharmaceutical labelling process, pharmacological mechanisms, dosimetry data in patients, and clinical results in terms of image contrast. PET imaging has demonstrated a good efficacy in tumour hypoxia imaging with both FMISO and Cu-ATSM, but FMISO has presented too slow an in vivo accumulation and a weak image contrast of the hypoxia area. Despite a less favourable dosimetry, 64Cu-ATSM appears superior in terms of imaging performance, calling for industrial and clinical development of this innovative radiopharmaceutical.