Inclusion Criteria:

• Male or female, 12 years of age or older.
• Have undergone an allo-HSCT from any donor source using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative conditioning regimens are eligible.
• Clinically suspected all grades acute or chronic GVHD as per Minnesota-Center for International Blood and Marrow Transplant Research (MN-CIBMTR) criteria, that is refractory or intolerant to corticosteroids, occurring after allo-HSCT with any conditioning regimen and any anti-GVHD prophylactic program. Clinical suspicion of GVHD by the treating physician is also sufficient. 
• Evidence of myeloid engraftment (e.g., absolute neutrophil count ≥ 1.0 × 10^9/L for 3 consecutive days if ablative therapy was previously used). Use of growth factor supplementation is allowed. 
• Evidence of platelet engraftment (i.e., platelets ≥ 20 × 10^9/L). 
• Eastern Cooperative Oncology Group (ECOG) performance status 0 to 3. 
• Be willing to avoid pregnancy or fathering children based on 1 of the following criteria: 
  • Women of non-childbearing potential (i.e., surgically sterile with a hysterectomy and/or bilateral oophorectomy OR ≥ 12 months of amenorrhea);
  • Woman of childbearing potential who has a negative serum pregnancy test at screening and who agrees to take appropriate precautions to avoid pregnancy (with at least 99% certainty) from screening through safety follow-up. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the patient and their understanding confirmed;
  • Man who agrees to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through safety follow-up. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the patient and their understanding confirmed.
• Able to provide written informed consent and/or assent from the patient, parent, or guardian.

 Exclusion Criteria: 

• Eligible for an existing and actively enrolling Incyte sponsored clinical trial for ruxolitinib for the treatment of GVHD. 
• Patients or legal guardians unable to review and sign informed consent form.
• Females who are pregnant or breastfeeding, and males and females who cannot comply with requirements to avoid fathering a child or becoming pregnant. 
• Patients with inadequate liver function (alanine aminotransferase above 4 × upper limit of normal (ULN) or direct bilirubin 4 × ULN and the laboratory abnormalities are considered to be due to underlying liver dysfunction) unless attributed to GVHD. 
• Patients with end stage renal function (creatinine clearance (CrCl) < 15 mL/min or glomerular filtration rate < 15 mL/min), regardless of whether hemodialysis is required. 
• Any underlying or current medical or psychiatric condition that, in the opinion of the treating physician, would place the patient at an unacceptable risk if he or she were to participate in the program. 
• Previous allergic reactions to Janus kinase (JAK) inhibitors or excipients. 
• Patients who are currently taking any anticancer therapy (e.g., chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, hormonal therapy, or tumor embolization). 
• Patients taking any secondary GVHD therapy due to insufficient response/progression on program treatment including, but not limited to, ibrutinib, filgotinib, and other off-label medications.
• Concomitant use of any JAK inhibitor.
• Initiating therapy with any investigational medication. 
• Presence of an active uncontrolled infection. An active uncontrolled infection is defined as hemodynamic instability attributable to sepsis or new symptoms, worsening physical signs, or radiographic findings attributable to infection. Persisting fever without signs or symptoms will not be interpreted as an active uncontrolled infection. 
• Known HIV infection. 
• Active hepatitis B virus (HBV) or hepatitis C virus infection that requires treatment or at risk for HBV reactivation. At risk for HBV reactivation is defined as hepatitis B surface antigen positive or anti-hepatitis B core antibody positive. Previous test results obtained as part of standard of care before allo-HSCT that confirm a patient is immune and not at risk for reactivation (i.e., hepatitis B surface antigen negative, surface antibody positive) may be used for purposes of eligibility.