Inclusion Criteria:
* Histological confirmation of WM; patients may have newly diagnosed, relapsed, or refractory disease; (definition: newly diagnosed; patients previously untreated for WM, relapse; patients who have received prior treatment for WM and now have disease recurrence; refractory; patients who have received anti-WM therapy and are noted to have progressive disease while on therapy, or those patients who demonstrated disease progression within 6 months of the last anti-WM treatment); NOTE: Ibrutinib naïve patients are allowed; if previously treated with ibrutinib, subject must have reached a response of at least stable disease (SD) and cannot have progressed while on ibrutinib; if subject stopped taking ibrutinib for reasons other than progression, they cannot have progressed for at least 6 months post last dose of ibrutinib
* Presence of measurable disease as defined by: presence of immunoglobulin M (IgM) paraprotein, measurable lymphadenopathy on imaging studies and/or physical exam, and/or bone marrow infiltration \> 10%
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0, 1, or 2
* Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 14 days prior to registration)
* Platelet count \>= 75,000/mm\^3 (obtained =\< 14 days prior to registration) (NOTE: platelet transfusions in order to help patients meet eligibility criteria are not allowed)
* Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration)
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless due to Gilbert's syndrome, in which case the direct bilirubin must be =\< 1.5 x ULN (obtained =\< 14 days prior to registration)
* Aspartate transaminase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN (obtained =\< 14 days prior to registration)
* Calculated creatinine clearance must be \>= 30 ml/min using the Cockcroft Gault formula (obtained =\< 14 days prior to registration)
* Negative pregnancy test done at screening and =\< 3 days (72 hours) prior to registration, for women of childbearing potential
* Provide written informed consent
* Willingness to provide mandatory blood specimens and bone marrow specimens for correlative research
* Willingness to return to enrolling institution for follow-up
Exclusion Criteria:
* Failure to have fully recovered (i.e., =\< grade 1 toxicity) from the reversible effects of prior treatment for WM
* Major surgical procedure (including open biopsy, excluding central line intravenous (IV) and port-a-cath placement) within =\< 14 days prior to initiating study treatment, or anticipation of the need for major surgery during the course of the study treatment
* Radiotherapy =\< 14 days prior to registration; if the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the ixazomib
* Systemic treatment, =\< 14 days before registration, with strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or St. John's wort
* Systemic anti-cancer therapy or participation in other clinical trials, including those with other investigational agents not included in this trial, =\< 28 days of registration and throughout the duration of active treatment in this trial
* Patients that have previously been treated with ixazomib, or participated in a study with ixazomib whether treated with ixazomib or not; prior bortezomib treatment is allowed as per: patients with prior exposure to bortezomib will be allowed if they do not have disease refractory to bortezomib)
* Central nervous system involvement (Bing-Neel syndrome)
* Infection requiring systemic antibiotic therapy or other serious infection =\< 7 days prior to registration
* Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, serious cardiac arrhythmia requiring medication (other than adequately rate-controlled atrial fibrillation), symptomatic congestive heart failure, unstable angina, stroke/transient ischemic attack (TIA) within the past 6 months or myocardial infarction within the past 6 months
* Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent
* Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib or ibrutinib, including difficulty swallowing
* History of any other prior malignancy; (NOTE: Exception to this are adequately treated non-melanoma skin cancers, any in situ cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for at least two years prior to study enrollment)
* Patient has \>= grade 2 peripheral neuropathy or grade 1 peripheral neuropathy with pain on clinical examination during the screening period
* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown
* Pregnant women
* Nursing women
* Men or women of child bearing potential (WCBP) who are unwilling to employ effective contraception; effective contraception would be defined as utilizing 2 simultaneous methods of contraception from the time of signing consent through 90 days after the last dose of the study drugs unless they agree to participate in true abstinence when this is in line with the preferred and usual lifestyle of the subject; (WCBP: A female who is sexually mature and who: \[1\] has not undergone a hysterectomy or bilateral oophorectomy; or \[2\] has not been naturally postmenopausal for at least 24 consecutive months \[i.e., has had menses at any time in the preceding 24 consecutive months\])
* Evidence of any other serious medical condition (such as psychiatric illness, infectious diseases, physical or laboratory findings) that may interfere with the planned treatment, affect compliance or place the patient at high risk from treatment-related complications or potentially interfere with the completion of the treatment as per the protocol
* Ongoing, active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive
* Liver disease with Child-Pugh class B or C liver dysfunction
* Current treatment with a combination of ibrutinib and strong CYP3A inhibitors
