Prospective Monitoring of Subjects With Biochemically Recurrent Prostate Cancer Using 18FDCFPyL

* INCLUSION CRITERIA: * History of primary treatment for prostate cancer (either surgery or radiation) * Serum PSA \>= 0.50 * Serum testosterone \>100 * Age \>=18 years * Men must agree to use highly effective contraception (surgical sterilization) for 7 days after every study agent administration. Note: abstinence, defined as no heterosexual sexual intercourse when this is in line with the preferred and usual lifestyle of the subject is also acceptable * The ability of a participant to understand and the willingness to sign a written informed consent document EXCLUSION CRITERIA: -Evidence of soft tissue disease on CT scan (or magnetic resonance imaging \[MRI\] as clinically indicated). NOTE: Lymph nodes \<= 1.5 cm in the shortest dimension are allowed. * Evidence of bone lesions on Tc99 bone scan * Prostatectomy within 1 year before the study intervention * Androgen deprivation therapy (ADT) within the 6 months before the study intervention * Systemic therapy for prostate cancer within the 6 months before the study intervention. Other investigational agents, excluding those involving standard of care chemotherapy, received within 6 months prior to the study intervention are allowed.