Inclusion Criteria:
* Advanced unresectable or metastatic histologically or cytologically confirmed adenocarcinoma of the biliary tract, including cholangiocarcinoma (intrahepatic or extrahepatic) and gallbladder carcinoma. Patients whose tumor have mixed histology but predominantly (\>50%) adenocarcinoma are allowed.
* Measurable defined by RECIST v1.1.
* No prior systemic treatment for advanced unresectable or metastatic BTC with the following exceptions:
* Neoadjuvant or adjuvant systemic therapy completed \> 6 months from planned C1D1.
* Up to two prior cycles of gemcitabine/cisplatin/anti-PD1 with no evidence of disease progression is allowed
* At least 18 years of age.
* ECOG performance status 0, 1, or 2
* Adequate bone marrow and organ function as defined below:
* Absolute neutrophil count ≥ 1.5 K/cumm
* Platelets ≥ 100 K/cumm
* Hemoglobin ≥ 9.0 g/dL
* Total bilirubin ≤ 1.5 x IULN or ≤ 3 x IULN in patients with documented Gilbert's syndrome
* AST(SGOT)/ALT(SGPT) ≤ 2 x IULN, unless there are liver metastases in which case AST and ALT ≤ 5.0 x IULN
* Creatinine clearance ≥ 35 mL/min by Cockcroft-Gault
* INR ≤ 1.5 and activated partial thromboplastin time (aPTT) ≤1.5 x IULN
* Creatinine phosphokinase (CPK) elevation at screening \< Grade 2 (CPK \< 2.5 x IULN).
* Patients on a cholesterol lowering statin must be on a stable dose with no dose changes within 3 weeks prior to study start.
* The effects of emavusertib on the developing human fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of the study, and 90 days after completion of the study.
* Ability to understand and willingness to sign an IRB approved written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants.
Exclusion Criteria:
* Current use or anticipated need for alternative, holistic, naturopathic, or botanical formulations used for the purpose of cancer treatment. Use of medical marijuana is permitted.
* A history of other malignancy with the exception of 1) malignancies for which all treatment was completed at least 2 years before registration and the patient has no evidence of disease; 2) or known indolent malignancies that do not require treatment and will likely not alter the course of treatment of BTC in the opinion of the investigator
* History of allogeneic organ or stem cell transplant.
* Currently receiving any other investigational therapeutic agents. Investigational tracers related to imaging studies are allowed with a 7 day-washout.
* Clinically active CNS metastasis; treated and asymptomatic metastasis allowed at the discretion of the sponsor/investigator or site PI. Radiotherapy to the brain must be completed \> 10 days prior to planned C1D1.
* Chemoradiation with curative intent within 6 months prior to C1D1 of study therapy.
* Palliative radiation therapy within 10 days prior to C1D1 of study therapy.
* A history of allergic reactions attributed to compounds of similar chemical or biologic composition to emavusertib, gemcitabine, cisplatin, durvalumab, or other agents used in the study.
* Concomitant use of drugs with a known risk of causing prolonged QTc (with exception of Zofran if needed for supportive care) and/or Torsades de Pointes or a history of risk factors for Torsades de Pointes.
* Presence of interstitial lung disease or pneumonitis ≥ G2 at time of screening.
* Administration of a live attenuated vaccine within 30 days prior to C1D1
* QTc (Fridericia) \>470ms on screening EKG.
* Gastrointestinal condition which could impair absorption of emavusertib or inability to ingest emavusertib in the opinion of the investigator.
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia in the opinion of the investigator.
* Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 7 days of C1D1.
* Patients with known HIV are eligible unless their CD4+ T-cell counts are \< 350 cells/mcL or they have a history of AIDS-defining opportunistic infection within the 12 months prior to registration. Concurrent treatment with effective ART according to DHHS treatment guidelines and in line with contraindicated concomitant medications is recommended.
* Participants with active, known, or suspected autoimmune disease. Participants with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, euthyroid participants with a history of Grave's disease (participants with suspected autoimmune thyroid disorders must be negative for thyroglobulin and thyroid peroxidase antibodies and thyroid stimulating immunoglobulin prior to first dose of study treatment), psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll after discussion with the sponsor-investigator or site PI.
* Participants with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days prior to the first dose of study treatment except for adrenal replacement steroid doses \> 10 mg daily prednisone equivalent in the absence of active autoimmune disease. Note: treatment with a short course of steroids (\< 5 days) up to 7 days prior to initiating study treatment is permitted. Inhaled intranasal, intra-articular, and topical steroid uses are permitted.
* History of grade 3 or greater rhabdomyolysis that did not completely resolve.
* Patients are unwilling to adhere to the lifestyle guidance
