Inclusion Criteria:
* 50 to 110 days post-transplant prior to registration
* Age ≥ 18 years
* HLA matched-related, matched unrelated donors (defined as 8/8 \[class I: HLA A, B, C, and class II: DRB1\]), or HLA-mismatched-unrelated donors (defined as 7/8 \[with single mismatch at class I: HLA A, B, C, or class II: DRB1\])
* Karnofsky performance status (PS) ≥ 70
* Hemoglobin ≥ 8.0 g/dL (untransfused) (obtained ≤ 7 days prior to registration)
* Absolute neutrophil count (ANC) ≥ 1000/mm\^3 (without growth factor support) (obtained ≤ 7 days prior to registration)
* Platelet count ≥ 50,000/mm\^3 (untransfused) (obtained ≤ 7 days prior to registration)
* Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) ≤ 1.5 x upper limit of normal (ULN) (obtained ≤ 7 days prior to registration)
* Total bilirubin ≤ 1.5 x ULN (unless it is due to Gilbert's syndrome or causes other than liver) OR alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 2 x ULN (unless it is due to Gilbert's syndrome or causes other than liver) (obtained ≤ 7 days prior to registration)
* Calculated creatinine clearance ≥ 40 ml/min using the Cockcroft-Gault formula (obtained ≤ 7 days prior to registration)
* Adequate cardiac and pulmonary function at baseline (may be based on pre-transplant vital organ work up):
* Cardiac evaluation to determine left ventricular ejection fraction (LV-EF) if there is any clinical reason (for example an ischemic event or hypovolemic shock) to suspect that the LV-EF was affected from the time of the prior measurement of baseline (required ≥ 45%)
* Pulmonary evaluation to determine adequate pulmonary function with a diffusion capacity of the lung for carbon monoxide (DLCO) ≥ 50% predicted value, forced expiratory volume in 1 second (FEV1) ≥ 50% predicted value and forced vital capacity (FVC) ≥ 50% predicted value
* Persons of childbearing potential must have negative serum pregnancy test ≤ 7 days prior to registration. Persons of non-reproductive potential are defined as follows: post-menopausal by history - no menses for ≥ 1 year; or status post (s/p) hysterectomy; or s/p bilateral tubal ligation; or history of bilateral oophorectomy
* All subjects agreeable to using both a highly effective method of birth control \[for example, implants, injectables, combined oral contraceptives, intrauterine devices (IUDs), or sterilized partner\] and a barrier method (e.g., condoms, vaginal ring, sponge, etc.) during the period of therapy and for 90 days after the last dose of study drug
* Provide written informed consent
* Willingness to return to enrolling institution for follow-up (during the active monitoring phase of the study).
* Note: During the active monitoring phase of a study (i.e., active treatment and clinical follow-up), participants must be willing to return to the consenting institution for follow-up
Exclusion Criteria:
* Uncontrolled acute GVHD at time of registration.
* Note: Uncontrolled is defined as unable to tolerate tapering down of steroids or other therapies or requiring additional therapies or increase in doses of prescribed therapies
* Evidence of NIH chronic GVHD preceding registration or at time of registration
* Relapsed/progressive disease compared to prior to transplant and prior to registration. In this case, baseline represents the baseline disease staging (if no other disease staging has been performed prior to enrollment); or a post-transplant disease staging if that represents the most immediate staging prior to enrollment. In the event that both had been performed, the latest one performed (i.e. the one closest in time to the enrollment to this trial) will be considered the baseline for comparison.
* Note: Relapse and progression definitions for each hematologic malignancy/ disorder will follow standard definition
* Uncontrolled active systemic fungal, viral, bacterial, or other infection Note: Infections are considered controlled if appropriate therapy has been instituted and at the time of registration have no signs of progression are present. Progression of infection is defined as hemodynamic instability attributable to sepsis, new symptoms, worsening physical signs or radiographic findings attributable to infection
* Unable to swallow capsules or impairment/disease significantly affecting gastrointestinal function that may significantly alter the absorption of the drugs (e.g., gastric bypass surgeries, Celiac or Whipple disease)
* Any of the following because this study involves) an agent that has known genotoxic, mutagenic and teratogenic effects:
* Pregnant persons
* Nursing persons
* Persons of childbearing potential who are unwilling to employ adequate contraception
* History of stroke or intracranial hemorrhage ≤ 6 months prior to registration
* Active involvement of the central nervous system with malignancy.
* Note: Previous central nervous system (CNS) involvement is allowed if clearance of CNS disease has been documented prior to registration
* Require anticoagulation with warfarin or other Vitamin K antagonists
* Any of the following prior therapies:
* Administration of anti-thymocyte globulin (or equivalent), alemtuzumab, or post transplant cyclophosphamide as part of the conditioning regimen or ≤ 1 month of allograft. Patients must not have received T-cell depletion or CD-34 selection
* Administration of a strong cytochrome P450 (CYP) 3A inhibitor ≤ 7 days prior to the first dose or subjects who require continuous treatment with a strong CYP3A inhibitor
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Patients known to have tested positive on HIV antibody test
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Chronic liver disease with hepatic impairment Child Pugh class B or C
* Active hepatitis B or C infection.
* Note: A detailed assessment of hepatitis B/C medical history and risk factors must be done at screening for all patients. hepatitis B immunoglobulin M antibody (HBcIgM Ab), hepatitis B surface antigen (HBsAg) and hepatitis C virus antibody (HCV Ab) screen (scrn) w/reflex testing are required at screening for all patients with a positive medical history based on risk factors and/or confirmation of prior hepatitis B virus (HBV) infection
* Receiving any chemotherapy, anticancer immunotherapy, experimental therapy, or radiotherapy is prohibited while the subject is receiving study treatment with ibrutinib. The sponsor-investigator must be notified in advance (or as soon as possible thereafter) of any instances in which prohibited therapies are administered.
* EXCEPTION 1: Patients will be allowed to receive antimicrobial prophylaxis appropriate for allogeneic HCT recipients, according to institutional standards of practice (SOP) or common clinical practice
* EXCEPTION 2: Patients will be allowed to receive maintenance therapy, if it had been planned prior to the allogeneic HCT for the purpose of reducing risk of relapse or progression of malignancy. Examples of post-transplant maintenance includes inhibitors of fms-like tyrosine kinase 3 (FLT-3), Isocitrate Dehydrogenase 1 (IDH-1), Isocitrate Dehydrogenase 12 (IDH-2) or hypomethylating agents (azacitidine or decitabine) and inhibitors of BCL-2.
* Other active malignancy ≤ 5 years prior to registration.
* EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix.
* NOTE: If there is a history of prior malignancy, they must not be receiving other treatment for their cancer
* History of myocardial infarction ≤ 6 months, or uncontrolled cardiac arrhythmias
