Inclusion Criteria:

* Phase 1 Part: Patients with pathologically confirmed advanced stage B-cell NHL (Ann Arbor stage 3 or 4) for whom R-CHOP is considered appropriate therapy; newly diagnosed DLBCL, newly diagnosed low grade B cell NHL, and previously treated low grade B cell NHL patients in first relapse after a prior treatment with non-anthracycline containing chemotherapy are allowed; double hit and transformed diffuse large B cell lymphoma are allowed

\* Allowed low grade B cell lymphomas will include follicular lymphoma any grade, marginal zone lymphoma including mucosa-associated lymphoid tissue (MALT) lymphoma, indolent mantle cell lymphoma and Waldenstrom's macroglobulinemia
* Phase 2 Part: Patients with pathologically confirmed newly diagnosed diffuse large B cell lymphoma (Ann Arbor stage 3 or 4); newly diagnosed double hit and transformed diffuse large B cell lymphoma are allowed
* Patients must have measurable disease, defined as at least one lesion above and below the diaphragm or stage 4 disease that can be accurately measured in at least one dimension; lymph nodes should be considered abnormal if the long axis is \> 1.5 cm, regardless of the short axis
* Allowed prior therapy:

* Newly diagnosed DLBCL and low grade B cell lymphoma: No prior therapy is allowed except steroids equivalent to maximum of prednisone 20 mg once daily for maximum of seven days prior to registration
* Relapsed/refractory low grade B cell lymphoma (only allowed in phase I): A minimum and maximum of one line of prior non-anthracycline containing therapy is allowed; prior localized radiation therapy is not considered a line
* For patients who have had prior chemotherapy or immunotherapy, at least 2 weeks must have elapsed between last dose and initial dose of RCHOP-selinexor; for patients treated with radio-immunotherapy, at least 12 weeks
* All races and ethnic groups are eligible for this trial
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 60%)
* Life expectancy of greater than 6 months
* Premenopausal female patients of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male patients must use an effective barrier method of contraception if sexually active with a female of child-bearing potential; acceptable methods of contraception are condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal; for both male and female patients, effective methods of contraception must be used throughout the study and for three months following the last dose
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients with DLBCL who have received chemotherapy or immunotherapy (except one week of steroids as described above) at any time point in the past for therapy of the DLBCL; patients with low grade B cell lymphomas who have received more than one prior line of chemotherapy or any anthracycline-containing therapy in the past for their low grade B cell lymphoma; localized radiation therapy does not count as a line of therapy
* Patients who are receiving any other investigational agents
* Patients with known brain metastases are excluded
* History of severe allergic reactions (as determined by treating physician) attributed to the drugs being used in the study
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, congestive heart failure (New York Heart Association \[NYHA\] class \>= 3 or left ventricular ejection fraction \< 45%), unstable angina pectoris, myocardial infarction within the last 3 months, clinically significant cardiac arrhythmia (i.e., ventricular tachycardia on anti-arrhythmia are excluded; 1st degree atrioventricular \[AV\] block or asymptomatic left anterior fascicular block \[LAFB\]/right bundle branch block \[RBBB\] permissible), or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant and lactating women are excluded
* Human immunodeficiency virus (HIV)-positive patients regardless of treatment are excluded; patients with evidence of active hepatitis B and hepatitis C infection with positive real time polymerase chain reaction (qPCR) are also excluded but patients with prior exposure to hepatitis B or C with negative qPCR are allowed
* Patients with severe intolerance to glucocorticoids
* Major surgery within 2 weeks of first dose of study drug
* Patients who are unable to swallow tablets, patients with malabsorption syndrome, or any other gastrointestinal (GI) disease or GI dysfunction that could interfere with absorption of study treatment
* Absolute neutrophil count (ANC) \< 1500 cells/mm\^3
* Platelet count \< 100,000/mm\^3
* Serum bilirubin \> 1.5 times the upper limit of normal (ULN) (except patients with Gilbert's syndrome: total bilirubin of \> 3 x ULN)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \> 2.5 times ULN
* Estimated creatinine clearance of \< 30 mL/min, calculated using the formula of Cockroft and Gault