Inclusion Criteria:
* Patients with Philadelphia (Ph)+ acute myeloid leukemia (AML) or myeloid accelerated phase (AP)-chronic myelogenous leukemia (CML) or blast phase (BP)-CML (either t\[9;22\] and/or BCR-ABL1 positive by fluorescent in situ hybridization or polymerase chain reaction). Both untreated and relapsed/refractory patients are eligible
* Performance status =\< 3 (Eastern Cooperative Oncology Group \[ECOG\] scale)
* Total serum bilirubin =\< 2 x upper limit of normal (ULN), unless due to Gilbert's syndrome, hemolysis or the underlying leukemia approved by the principal investigator (PI)
* Alanine aminotransferase (ALT) =\< 1.5 x ULN, unless due to the underlying leukemia approved by the PI
* Aspartate aminotransferase (AST) =\< 1.5 x ULN unless due to the underlying leukemia approved by the PI
* Creatinine clearance \>= 30 mL/min
* Serum lipase =\< 1.5 x ULN
* Amylase =\< 1.5 x ULN
* Ability to swallow
* Signed informed consent
Exclusion Criteria:
* Active serious infection not controlled by oral or intravenous antibiotics (e.g. persistent fever or lack of improvement despite antimicrobial treatment)
* History of acute pancreatitis within 6 months of study or history of chronic pancreatitis
* Uncontrolled hypertriglyceridemia (triglycerides \> 450 mg/dL)
* Active secondary malignancy that in the investigator's opinion will shorten survival to less than 1 year
* Active grade III-V cardiac failure as defined by the New York Heart Association criteria
* Clinically significant, uncontrolled, or active cardiovascular disease, specifically including, but not restricted to:
* Myocardial infarction (MI), stroke, revascularization, unstable angina or transient ischemic attack within 6 months
* Left ventricular ejection fraction (LVEF) less than lower limit of normal per local institutional standards prior to enrollment
* Diagnosed or suspected congenital long QT syndrome
* Clinically significant atrial or ventricular arrhythmias (such as uncontrolled, clinically significant atrial fibrillation, ventricular tachycardia, ventricular fibrillation, or torsades de pointes) as determined by the treating physician
* Prolonged corrected QT (QTc) interval on pre-entry electrocardiogram (\> 480 msec) unless corrected after electrolyte replacement
* History of venous thromboembolism including deep venous thrombosis or pulmonary embolism within the past 3 months, excluding line-associated deep venous thrombosis (DVT) of the upper extremity
* Uncontrolled hypertension (diastolic blood pressure \> 100 mmHg; systolic \> 150 mmHg)
* Consumed grapefruit, grapefruit products, Seville oranges, or star fruit within 3 days prior to starting venetoclax
* Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or patient has rapidly progressive disease judged to be life-threatening by the investigator. Prior recent treatment with corticosteroids, hydroxyurea, or a Food and Drug Administration (FDA)-approved BCR-ABL tyrosine kinase inhibitor (TKI) is permitted
* Pregnant and lactating women will not be eligible; women of childbearing potential should have a negative pregnancy test prior to entering on the study and be willing to practice methods of contraception throughout the study period. Women do not have childbearing potential if they have had a hysterectomy or are postmenopausal without menses for 12 months. In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control
