Using blood tests to tailor radiation therapy for HPV-positive throat cancer

Inclusion Criteria:

* PRE-REGISTRATION (optional): Provide written informed consent
* Age \>= 18 years
* Histological confirmation of squamous cell carcinoma originating from or suspected to be originating from the oropharynx
* Plan for gross total surgical resection via trans oral surgery with curative intent and at least unilateral neck dissection OR chemoradiotherapy with cisplatin. Note: The patient must be cisplatin eligible even if an alternate is used due to drug shortage
* Absence of distant metastases on standard diagnostic work-up =\< 16 weeks prior to registration. (Chest CT or PET/CT)
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 1
* Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only
* Ability to complete questionnaire(s) by themselves or with assistance
* Provide written informed consent
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)
* Willing to provide blood samples for correlative research purposes, including anonymous shipment of samples to for NavDx testing

Exclusion Criteria:

* Any of the following:

  * Pregnant women
  * Nursing women
  * Men or women of childbearing potential who are unwilling to employ adequate contraception
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Immunocompromised patients and patients known to be human immunodeficiency virus (HIV)+
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Other active malignancy =\< 5 years prior to registration. EXCEPTIONS: Nonmelanotic skin cancer or carcinoma-in-situ of the cervix, or prostate or localized endometrioid endometrial cancer. NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment for their cancer
* Prior history of radiation therapy to the affected site
* Prior systemic chemotherapy in the last 5 years
* Contraindication to radiation therapy as determined by the treating team
* History of allergic reaction to docetaxel
* Receiving any medications or substances which in the opinion of the investigators would interfere with treatment. Examples could include strong inhibitors of cytochrome P450 3A4 (CYP3A4) at oncologist discretion
* Severe pre-existing ototoxicity or neuropathy that would, in the opinion of the investigator, preclude the use of cisplatin chemotherapy
* cT4 primary tumor

  * NOTE: Patients with no intermediate risk factors after surgery, low risk patients, as defined by T1, T2, tumors with lymph node less than 3cm, no intermediate or high-risk factors such as lymphatic invasion (LVSI), extranodal extension (ENE), perineural invasion (PNI), positive margin, will be withdrawn from study and be observed per current clinical standard of care. Patients found to be both HPV negative and p16 negative will be withdrawn from study.
  * Patients found to have HPV non 16 type, or HPV detectability in blood less than \<20tumor tissue modified viral (TTMV) will not be candidates for de-escalation in Groups 1 and 2 and will be treated in Group 3 unless otherwise meeting criteria for low risk. They will receive 60 Gy +/- cisplatin or acceptable alternate regimen when drug shortages of cisplatin exist. If treated primarily with chemoradiation (chemoRT) (Group 4), these patients will not be candidates for de-escalation if TTMV is \< 50 TTMV but can remain on study receiving 70 Gy with all corresponding correlative studies applying
  * Patients with unknown (radiologic/clinically occult) primaries but neck adenopathy suspected to be HPV associated oropharyngeal carcinoma can be registered to go on study for Groups 1-3. Should after primary resection, no primary tumor be identified, the patient will be withdrawn from study and be treated per institutional standard of care. Group 4 patients must have an identifiable (clinically or radiologically apparent) primary tumor
  * All treatment primarily, including surgery and chemotherapy will be performed at the enrolling institution