Inclusion Criteria:
* Ability to understand and the willingness to sign a written informed consent document
* Age \>= 18 years at time of informed consent. Persons of all genders and gender identities, and members of all races and ethnic groups will be included
* Morphologically documented relapsed/refractory (R/R) AML or R/R secondary AML (sAML) that has progressed after at least 1 prior therapy for AML
* Prior treatment with venetoclax and azacitidine is allowed
* Treatment with hydroxyurea will not be considered a line of therapy
* Patients with morphologically documented myelodysplastic syndrome (MDS) that has progressed on hypomethylating agent (HMA) therapy also will be considered if the patient is ineligible for induction with intensive chemotherapy (IC), defined for this study as meeting one or more of the following criteria:
* Severe cardiac disorder (e.g., congestive heart failure requiring treatment, left ventricular ejection fraction (LVEF) of ≤ 50%, or chronic stable angina)
* Severe pulmonary disorder, certified by the managing physician
* Creatinine clearance of \< 45 ml/min or
* Hepatic disorder with total bilirubin \> 1.5 x upper limit of normal (ULN)
* Eastern Cooperative Oncology Group (ECOG) equal to 2
* Other comorbidity(ies) judged to be incompatible with high dose chemotherapy by the managing physician will be considered, at the discretion of the principal investigator (PI)
* ECOG performance status 0 to 2
* Persons of childbearing potential (PCBP) must have a negative serum or urine pregnancy test within 14 days prior to start of study drug administration
* Patients must agree to use an adequate method of contraception while on study treatment and for 120 days after the last dose of ruxolitinib for Arm 1 and 6 months after the last dose of azacitidine for Arm 2
* Must be able to take and absorb oral medications
* Creatinine clearance ≥ 30 mL/min; calculated by the Cockcroft Gault formula or measured by 24 hour urine collection
* Total serum bilirubin ≤ 1.5 x ULN unless thought to be due to leukemic involvement
* Serum aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) ≤ 3.0 x ULN unless thought to be due to leukemic involvement
Exclusion Criteria:
* Diagnosis of acute promyelocytic leukemia (APL or AML M3 subtype)
* Active central nervous system involvement with AML
* Chemotherapy or therapy with a non-investigational agent other than a biologic intended to within 1 week of the planned start of study therapy, with the exception of hydroxyurea for cytoreduction of proliferative disease, or at the discretion of the principal investigator (PI)
* Therapy with a non-biologic investigational agent within 14 days or 5 half lives, whichever is longer, of the planned start of study therapy, or for the period recommended by the institution's research pharmacy service, or at the discretion of the PI
* Therapy with a biologic investigational or non-investigational agent (e.g., monoclonal antibody) within 30 days of the planned start of study therapy, or for the period recommended by the institution's research pharmacy service, or at the discretion of the PI
* Concurrent active malignancy with expected survival of less than 1 year, at the discretion of the investigator. For example, candidates with treated skin cancers, prostate cancer, breast cancer, etc. without metastatic disease are candidates for therapy since their expected survival exceeds that of relapsed or refractory AML
* Clinically significant graft versus host disease (GVHD) or active GVHD requiring initiation or escalation of treatment within 28-day screening period
* Participants with rapidly progressive disease (defined by blast count doubles within 48 hours) or organ dysfunction
* Documented cardiac insufficiency (e.g., symptomatic heart failure, left ventricular ejection fraction of ≤ 40%)
* Symptomatic shortness of breath or patient requires supplemental oxygen support
* Clinically significant coagulation abnormality, such as disseminated intravascular coagulation
* Known history of cerebrovascular accident, myocardial infarction, or intracranial hemorrhage within 2 months of enrollment
* Known clinically significant liver disease defined as ongoing drug-induced liver injury, chronic active hepatitis C (hepatitis C virus \[HCV\]), chronic active hepatitis B (hepatitis B virus \[HBV\]), alcoholic liver disease, non-alcoholic steatohepatitis, primary biliary cirrhosis, extrahepatic obstruction caused by cholelithiasis, cirrhosis of the liver, portal hypertension, or history of autoimmune hepatitis
* Untreated HIV or active hepatitis C detectable by polymerase chain reaction (PCR), or chronic hepatitis B (patients positive for hepatitis B core antibody who are receiving intravenous immunoglobulin therapy \[IVIG\] are eligible if hepatitis B \[HepB\] PCR is negative)
* Per PI discretion, active infection that is not well controlled by antibacterial or antiviral therapy
\*Patients with a known history of tuberculosis (TB; Mycobacterium tuberculosis) are not eligible for participation. At investigator discretion, latent TB test should be performed for individuals considered to be at high-risk (e.g., immune compromised, persons that have traveled to, or emigrated from, regions with high rates of TB)
* Clinically significant surgery within 2 weeks of enrollment
* Unwillingness to receive infusion of blood products
* Requires use of medications interact with study drug and that cannot be terminated or adjusted. Use of the following therapies requires review by the sponsor investigator:
* Strong and moderate CYP3A inhibitors
* Strong and Moderate CYP3A inducers
* Patients with uncontrolled white blood cell count (defined as \> 50 K/mm\^3 and not controlled with hydroxyurea)
* Patients with known sensitivity to ruxolitinib, venetoclax, or azacitidine
* Since it is unknown whether ruxolitinib, venetoclax, or azacitidine (or their metabolites) are excreted in human milk and because of the potential for serious adverse reactions in the nursing infant, breastfeeding concurrent with study participation is prohibited
