Inclusion Criteria:

* Documented informed consent of participant and/or legally authorized representative
* Agreement to allow the use of archival tissue from diagnostic tumor biopsies will be retrieved and submitted post-enrollment

* If unavailable, exceptions may be granted with study principal investigator (PI) approval.
* Eastern Cooperative Oncology Group (ECOG) status =\< 2
* Histologically confirmed mature peripheral T-cell or natural killer (NK)-cell lymphoma per World Health Organization (WHO) classification, including:

* Anaplastic lymphoma kinase (ALK)-positive anaplastic large cell lymphoma (ALCL) with international protein index (IPI) of 2 or higher (must have bulky \[defined as mass \>= 10 cm\] stage II, or stage III-IV disease)
* ALK-negative ALCL

* NOTE: Per amendment dated 05-10-19, ALCL will no longer be eligible except for Canada.
* PTCL-not otherwise specified (NOS)
* Angioimmunoblastic T-cell lymphoma (AITL)
* Adult T-cell lymphoma/leukemia (ATLL)
* Enteropathy-associated T-cell lymphoma (EATL)
* Hepatosplenic T-cell lymphoma
* CD30-positivity (e.g. at least 1%) by immunohistochemistry confirmed by hematopathology review at the participating institution
* Measurable disease of at least 1.5 cm on computed tomography (CT) or positron emission tomography (PET)-CT scan
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3

* Exception: unless documented bone marrow involvement by lymphoma
* Platelets \>= 50,000/mm\^3

* Exception: unless documented bone marrow involvement by lymphoma
* Total serum bilirubin =\< 1.5 x upper limit of normal (ULN) OR if hepatic involvement by lymphoma: =\< 3 x ULN for Gilbert's disease or documented hepatic involvement by lymphoma
* Aspartate aminotransferase (AST) =\< 2 x ULN OR if hepatic involvement by lymphoma: AST =\< 5 x ULN
* Alanine aminotransferase (ALT) =\< 2 x ULN OR if hepatic involvement by lymphoma: ALT =\< 5 x ULN
* Creatinine clearance of \>= 60 mL/min per the Cockcroft-Gault formula
* Left ventricular ejection fraction (LVEF) \>= 45%
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Agreement by WOCBP and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy; childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Prior treatment of PTCL with systemic anti-lymphoma therapies, investigational agents, radiation

* Exception: May have received 1 cycle of CHOP-like therapy (e.g. CHOP, CHOEP, EPOCH) or 1 cycle of CHP-BV; these participants must initiate day 1 cycle 1 of study therapy (CHEP-BV) no less than 19 days from prior CHOP-like or CHP-BV therapy; Patients who received 1 cycle of CHOP-like or 1 cycle of CHP-BV therapy prior to initiating induction with CHEP-BV are allowed to receive only 5 cycles of CHEP-BV instead of 6 cycles, per investigator's discretion
* History of another primary invasive cancer, hematologic malignancy, or myelodysplastic syndrome that has not been in remission for at least 3 years.

* Exceptions: Non-melanoma skin cancer and in situ cervical cancer
* Symptomatic cardiac disease (including symptomatic ventricular dysfunction, symptomatic coronary artery disease, and symptomatic arrhythmias), cerebrovascular event/stroke or myocardial infarction within the past 6 months
* Central nervous system involvement by lymphoma, including leptomeningeal involvement
* History of progressive multifocal leukoencephalopathy (PML)
* Active \>= grade 3 viral, bacterial, or fungal infection within 2 weeks prior to day 1 of protocol therapy
* Any known human immunodeficiency virus (HIV) infection, hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection
* Baseline peripheral neuropathy \>= grade 2 or patients with the demyelinating form of Charcot-Marie-Tooth syndrome
* Known severe hypersensitivity to any study related agent excipient(s)
* Females only: pregnant or breastfeeding
* Any other condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)