• Measure predictive accuracy of the change in PSMA PET with respect to the time to biochemical progression [ Time Frame: start of treatment to the first PSA level above 0.2 ng/ml, up to 100 months ]
• Measure predictive accuracy of the change in PSMA PET with respect to the time to metastasis [ Time Frame: Time from the start of treatment to evidence of systemic disease on bone scan or CT/MRI, up to 100 months ]
• Measure predictive accuracy of the change in PSMA PET with respect to overall survival time. [ Time Frame: Time from the start of treatment to date of death from any cause, assessed up to up to 100 months ]

• Prostate Cancer
• Prostate Neoplasm
• Prostate Adenocarcinoma
• Prostate Cancer Metastatic
• Metastatic Prostate Cancer

• Drug: 18F-DCFPyL-iPSMA
  Participants will be injected intravenously with a bolus of 7-10 mCi of 18F-DCFPyL.
• Drug: 68Ga-HBED-iPSMA
  Participants will be injected intravenously with a bolus of 3-8 mCi of 68Ga-HBED-iPSMA
• Diagnostic Test: PET/CT scan
  The baseline PSMA PET scan may be performed externally or at MSKCC, but all follow-up imaging must be performed at MSKCC. Approximately 60-90 minutes after intravenous injection of radiotracer, patients will be scanned from the mid-skull to the mid-thigh. Imaging will start with a low-dose CT for attenuation correction, followed by a PET scan. Upon completion of imaging and at the discretion of the investigator, the patient may be asked to void and get back in the scanner for 1 additional image of the pelvis.This additional image allows investigator's to see an unobstructed view of the prostate/prostate bed

Inclusion Criteria:

• Patients with histologically confirmed prostate cancer, that is either: newly diagnosed OR progressive as defined by standard PCWG3 criteria. note that metastatic disease is defined by either bone scintigraphy or by CT or MRI, or a combination of these tests, but not exclusively by molecular imaging criteria.

Patients with newly diagnosed localized or metastatic prostate cancer are eligible, provided standard imaging (either bone scintigraphy, CT or MRI) demonstrates evidence of radiographic disease

Patient with progressive disease that is non-metastatic are eligible by biochemical progression: A minimum of three rising PSA values from a baseline that are obtained 1 week or more apart, or 2 measurements 2 or more weeks apart

Patients with progressive disease that is metastatic are eligible either by biochemical progression or radiographic progression or both

Patients are permitted to have had up to 2 months of prior hormonal therapy before entering this trial (and many therapeutic trials) and therefore, their progression criteria would apply to their pre-treatment imaging and PSA parameters

• Karnofsky performance status of >/= 50 (or ECOG/WHO equivalent)
• Male (or transgender female) > 18 years of age
• Patient must be able to understand and willing to sign a written informed consent document
• Patient is anticipating starting a therapeutic strategy following imaging

Exclusion Criteria:

• Patient undergoing active treatment for non-prostate malignancy, other than skin basal cell or cutaneous superficial squamous cell carcinoma that has not metastasized and non-invasive bladder cancer
• Unable to lie flat, still or tolerate a PET scan