• 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