Inclusion Criteria:

          -  Relapsed or refractory B-ALL due to receive salvage 1, 2, 3, 4, 5, or 6; half of the
             patients, i.e. 5 out of the first 10 patients, and 5 out of 10 patients thereafter,
             need to be in earlier line of salvage therapy, defined as 1st, 2nd, or 3rd line of
             salvage therapy; Philadelphia chromosome-positive (Ph+) B-ALL patients must have
             failed treatment with at least 1 second generation tyrosine kinase inhibitor; patients
             in salvage 1 with late relapse should be deemed poor candidates for reinduction with
             initial therapy; patients with ALL of T cell origin (T-ALL) can not be treated

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Total bilirubin =< 1.5 × upper limit of normal (ULN) (unless Gilbert's syndrome or
             disease infiltration of the liver is present)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.0 × institutional ULN

          -  Creatinine clearance (Cockcroft-Gault) greater than or equal to 30 mL/min or estimated
             (est) glomerular filtration rate (GFR) greater than or equal to 30 mL/min/1.73 m^2

          -  For any surgery or invasive procedure requiring sutures or staples for closure,
             ibrutinib should be held at least 7 days prior to the intervention and should be held
             at least 7 days after the procedure, and restarted at the discretion of the
             investigator when the surgical site is reasonably healed without serosanguineous
             drainage or the need for drainage tubes

          -  Bone marrow involvement with >= 5% lymphoblasts, peripheral blast count less than
             5,000 per uL

          -  Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry and for
             the duration of study participation; should a woman become pregnant or suspect she is
             pregnant while she or her partner is participating in this study, she should inform
             her treating physician immediately; female patients need a negative serum or urine
             pregnancy test within 14 days of study start (applies only if patient is of
             childbearing potential); non-childbearing is defined as >= 1 year postmenopausal or
             surgically sterilized; men treated or enrolled on this protocol must also agree to use
             adequate contraception prior to the study, for the duration of study participation,
             and 4 months after completion of ibrutinib administration

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Patients who receive other chemotherapy; patients must have been off previous therapy
             for >= 2 weeks and must have recovered from clinically significant toxicity (to grade
             1 or less) of all previous therapy prior to enrollment (consent signing) with the
             following exceptions: steroids, hydroxyurea, oral mercaptopurine, methotrexate,
             vincristine (including prophylactic intrathecal medication), thioguanine, and tyrosine
             kinase inhibitors are permitted within 2 weeks of randomization as maintenance or to
             reduce the peripheral blood blast counts; during ibrutinib therapy, only steroids and
             hydroxyurea are permitted to reduce peripheral blood blast counts; patients who have
             had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin
             C) prior to entering the study or those who have not recovered from adverse events due
             to agents administered more than 2 weeks earlier

          -  Patients who are receiving any other investigational agents

          -  Active central nervous system (CNS) leukemia, as defined by unequivocal morphologic
             evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local
             treatment for active disease within the prior 28 days, symptomatic CNS leukemia (i.e.,
             cranial nerve palsies or other significant neurologic dysfunction) within 28 days;
             prophylactic intrathecal medication is not a reason for exclusion; patients with known
             brain metastases should be excluded from this clinical trial

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to ibrutinib

          -  Concomitant use of drugs that strongly inhibit cytochrome P450, family 3, subfamily A,
             polypeptide 4/5 (CYP3A4/5)

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection or an infection requiring systemic antibiotics, symptomatic congestive heart
             failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social
             situations that would limit compliance with study requirements

          -  Pregnant and breastfeeding women are excluded from this study; breastfeeding should be
             discontinued if the mother is treated with ibrutinib

          -  Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
             therapy are eligible, unless the patient's cluster of differentiation (CD)4 count is
             below the institutional lower limit of normal, or the patient is taking prohibited
             CYP3A4/5 strong inhibitors or inducers

          -  Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenic purpura (ITP)
             resulting in (or as evidenced by) declining platelet or hemoglobin (Hgb) levels within
             the 4 weeks prior to first dose of study drug

          -  Presence of transfusion-dependent thrombocytopenia

          -  Prior exposure to ibrutinib

          -  History of prior malignancy, with the exception of the following:

               -  Malignancy treated with curative intent and with no evidence of active disease
                  present for more than 3 years prior to screening and felt to be at low risk for
                  recurrence by treating physician

               -  Adequately treated non-melanomatous skin cancer or lentigo maligna melanoma
                  without current evidence of disease

               -  Adequately treated cervical carcinoma in situ without current evidence of disease

          -  Burkitt's or mixed lineage leukemia, T cell ALL

          -  Isolated extramedullary relapse (i.e., testicular or CNS)

          -  Patients with a cardiac ejection fraction (as measured by either multi gated
             acquisition scan [MUGA] or echocardiogram) < 45% are excluded; currently active
             clinically significant cardiovascular disease such as uncontrolled arrhythmia,
             congestive heart failure, any class 3 or 4 cardiac disease as defined by the New York
             Heart Association Functional Classification, or history of myocardial infarction
             within 6 months prior to first dose with study drug

          -  Unable to swallow capsules, or disease significantly affecting gastrointestinal
             function and/or inhibiting small intestine absorption, such as malabsorption syndrome,
             resection of the small bowel, or poorly controlled inflammatory bowel disease
             affecting the small intestine

          -  Serologic status reflecting active hepatitis B or C infection; patients that are
             hepatitis B core antibody positive but antigen negative will need a negative
             polymerase chain reaction (PCR) prior to enrollment; (hepatitis B antigen or PCR
             positive patients will be excluded;) (this may not be a necessary exclusion for an
             ibrutinib monotherapy protocol)

          -  History of stroke or intracranial hemorrhage within 6 months prior to enrollment

          -  Current life-threatening illness, medical condition, or organ system dysfunction
             which, in the Investigator's opinion, could compromise the patient's safety, or put
             the study at risk; any other severe concurrent disease, or have a history of serious
             organ dysfunction or disease involving the heart, kidney, liver or other organ system
             that may place the subject at undue risk to undergo therapy with ibrutinib

          -  Any serious medical condition, laboratory abnormality, or psychiatric illness that
             places the subject at unacceptable risk if he/she were to participate in the study

          -  Received anticoagulation therapy with warfarin or equivalent vitamin K antagonists
             within the last 28 days

          -  Evidence of clinically significant bleeding diathesis or coagulopathy

          -  Major surgical procedure, open biopsy, or significant traumatic injury, within 28 days
             prior to day 1, anticipation of need for major surgical procedure during the course of
             the study; (minor surgical procedures, fine needle aspirations or core biopsies within
             7 days prior to day 1; bone marrow aspiration +/- biopsy is allowed)

          -  Prior allogeneic stem cell transplant in previous 3 months