In present days positron emission tomography combined with X-ray computed tomography (PET/CT) is a highly informative, actively developing method of visualization in oncology, and in particular in oncourology. It is widely used to determine the localization of biochemical recurrence (BR) of prostate cancer (PCa). This survey article presents modern trends and prospects of the development of PET visualization of BR of PCa. It shows the diagnostic capabilities of PET/CT with various radiopharmaceuticals, including ligands for prostate-specific membrane antigen (PSMA), their main advantages and disadvantages. Brief historical information, the evolution of radiopharmaceuticals based on ligands to PSMA as the most promising group of radiopharmaceuticals are provided in the article. The biochemical basis of visualization, the main difficulties and possible errors in the interpretation of data, as well as the ways of overcoming them proposed by the researchers are highlighted.