Trial of Third Party Donor Derived CMVpp65 Specific T-cells for The Treatment of CMV Infection or Persistent CMV Viremia After Allogeneic Hematopoietic Stem Cell Transplantation

Inclusion Criteria: * Each patient must satisfy at least one of the following criteria: 1. The patient must have a clinically documented condition associated with CMV (e.g. interstitial pneumonia, hepatitis, retinitis, colitis) Or 2. The patient must have microbiological evidence of CMV viremia or tissue invasion as attested by viral culture, or detection of levels of CMV DNA in the blood or body fluids consistent with CMV infection. * Patient must also satisfy at least one of the following criteria: 1. The patient's CMV infection is clinically progressing or CMV viremia is persistent or increasing (as evidenced by quantitation of CMV DNA in the blood) despite two weeks induction therapy with antiviral drugs. Or 2. The patient has developed CMV viremia as attested by viral culture, or detection of levels of CMV DNA in blood or body fluids while receiving prophylactic doses of antiviral drugs to prevent CMV infection post transplant. Or 3. The patient is unable to sustain treatment with antiviral drugs due to drug associated toxicities (e.g. myelosuppression \[ANC\< 1000μl/ml without GCSF support\] or nephrotoxicity \[corrected creatinine clearance ≤ 60 ml/min/1.73 m\^2 or serum creatinine \> 2 mg/dl\]) CMV infections are life threatening, and may involve multiple organ systems such as the lungs, liver, gastrointestinal tract, hematopoietic and central nervous systems. Antiviral drugs used for treatment may also compromise renal and hematopoietic function. Therefore, dysfunctions of these organs will not affect eligibility for this protocol. * Patients must meet the following clinical criteria to receive CMVpp65-CTL infusions 1. Stable blood pressure and circulation, not requiring pressor support 2. Evidence of adequate cardiac function as demonstrated by EKG and/or echocardiography. 3. A life expectancy of at least 3 weeks, even if requiring artificial ventilation. 4. There are no age restrictions * Patient must also satisfy at least one of the following criteria: 1. The patient's HCT donor has not been previously infected by or sensitized to CMV (e.g. a cord blood transplant or a marrow or PBSC transplant from a seronegative donor). 2. The patient's HCT donor, if seropositive, is either not available or not willing to provide leukocytes for generation of CMV-specific T-cells. 3. There are CMVpp65-specific T-cells available in appropriate doses in the MSKCC Adoptive Immune T-cell Therapy Bank that are matched with the patient for 1 HLA allele and that exhibit CMVpp65-specific cytotoxic activity that is restricted by an HLA allele shared by the patient Exclusion Criteria: * Patients requiring high doses of glucocorticosteroids (≥ 0.3 mg/kg prednisone or its equivalent) * Patients who are moribund * Patients with other conditions not related to CMV infection (e.g. uncontrolled bacterial sepsis or invasive fungal infection) which are also life-threatening and which would preclude evaluation of the effects of a T-cell infusion. * Patients who are pregnant