Brief Summary: Background: Prostate cancer is the second leading cause of cancer deaths in American men. When prostate cancer is confined to the prostate there is a high chance of cure. However, it is outside the prostate or comes back after treatment, additional therapy may be needed. Current methods of imaging prostate cancer are limited. Researchers want to see if a radiotracer called 18F-DCFPyL can identify prostate cancer in patients who have a high risk of cancer spreading outside the prostate or who have signs of recurrent cancer after treatment. Objectives: To see if the radiotracer 18F-DCFyL can help identify prostate cancer in the body before or after therapy. Eligibility: Men ages 18 and older who have prostate cancer that has been newly diagnosed, or has relapsed after radiation or surgery Design: Participants will be divided into 2 groups. * Group 1 will be men with cancer that has been newly diagnosed as high risk by their doctor who are scheduled to have prostate removal surgery or undergo biopsy before radiation therapy. * Group 2 will be men who have presumed prostate cancer relapse after prostate removal surgery or radiation therapy. Both groups will have scans taken. Participants will lie still on a table in a machine that takes pictures of their body. 18F-DCFyL will be injected by intravenous (IV) line. Participants will be contacted for follow-up after scans. Participants in Group 1 may have surgery to remove their prostate gland or a biopsy to remove some prostate tissue. This procedure will be standard of care and is not a part of this study. They will also have an extra MRI scan of their prostate. For this, a tube, called an endorectal coil, will be placed in their rectum. Other tubes may be wrapped around the inside of their pelvis. A contrast agent will be given by IV. Participants in Group 2 may also undergo an MRI of the pelvis and may have a biopsy of abnormalities found on the 18F-DCFyL scan. Participants will have data about their prostate cancer collected for up to 1 year.

Detailed Description: Background: * Prostate cancer (PCa) is the second leading cause of cancer death in American men. * Patients with high risk but apparently localized disease are often understaged because disease beyond the prostate is not well detected and thus leads to overtreatment with prostatectomy * Recurrence of PCa after surgery or radiation is very common and sometimes progresses to death. * Early intervention for recurrence has been shown to be of benefit but current methods of localizing recurrence are either insensitive (CT), non-specific (MRI) or both (bone scan). Many prostate cancers express the prostate specific membrane antigen (PSMA) a transmembrane protein with NAALADase (N-acetylated-alpha-linked-acidic dipeptidase) and folate hydrolase enzymatic activity. PSMA is also expressed in angiogenesis but otherwise has limited expression in normal tissue. * An initial test of 18F-DCFBC, a first-generation PET agent targeting PSMA, in patients with advanced local disease and biochemically recurrent prostate cancer demonstrated the potential of PET to detect sites of recurrence but it was hampered by excessive blood pool activity. * (18)F-DCFPyL, a second generation PSMA PET agent, binds with high affinity to PSMA yet clears rapidly from the blood pool and thus, whole-body PET imaging with this agent, may provide a new tool in staging high risk cancers and detecting recurrent disease. Primary Objective: -To assess the ability of 18F-DCFPyL to accurately stage high-risk primary prostate cancer and detect sites of recurrent prostate cancer. Eligibility: * Age \>=18 years old * ECOG 0-2 * Histologically confirmed adenocarcinoma of the prostate * Patients fit criteria for one of the following categories: * Cohort 1: known localized high risk prostate cancer (PSA \>10, Gleason 8-10 or clinical stage \>T2c) with evidence of disease on standard imaging or --Cohort 2: nonspecific or no evidence of disease on standard imaging modality AND biochemical prostate cancer relapse with a PSA \> 0.2 ng/ml Design: * This is a single site study enrolling a total of 395 patients * All subjects will undergo 18F-DCFPyL injection and whole body PET/CT imaging, performed 2 hours (+/- 15 minutes) post 18F-DCFPyL injection. * Up to 10 eligible patients in either cohort 1 or 2 will receive an additional (18)F-DCFPyL PET/CT scan within 1 month of the first study immediately after unilateral salivary gland cannulation and an infusion of unlabeled DCFPyL or PSMA-11 into the cannulated gland. * Patients from cohort 2 who have a positive 18F-DCFPyL PET/CT scan at any time may also have a one-time 18F-FDG PET/CT within 30 days of the positive 18F-DCFPyL PET/CT. * All patients will undergo a standard of care, clinical multiparametric MRI in the NCI Molecular Imaging Clinic within 4 months of the PET scan. * The patients will be followed yearly for 4 years by chart review, phone-call, email or any other NIH approved platform for PSA relapse and radiologic evidence of metastatic disease. Additional (18)F-DCFPyL might be performed during the subject s follow up period if there has been a considerable change in patient status (progression or response) based on PSA value, symptomatology, bone scan or CT findings.