Single Agent Regorafenib in Refractory Advanced Biliary Cancers

Inclusion Criteria: * Histologically or cytologically documented carcinoma primary to the intra- or extra-hepatic biliary system or gall bladder with clinical and/or radiologic evidence of unresectable, locally advanced or metastatic disease. Patients with ampullary carcinoma are not eligible. * Have failed no more than 2 prior lines of systemic chemotherapy for advanced biliary cancer. Patients who received adjuvant chemotherapy and had evidence of disease recurrence within 6 months of completion of the adjuvant treatment are also eligible. If patient received adjuvant treatment and had disease recurrence after 6 months, they will only be eligible after failing one line of systemic chemotherapy used to treat the disease recurrence. * Eastern Cooperative Oncology Group (ECOG) Performance Status Assessment of 0 or 1 * Measurable and non-measurable disease will be allowed. * Must not have been treated with any vascular endothelial growth factor (VEGF) inhibitors. Prior 5-Fluorouracil (5-FU) or capecitabine treatment is allowed only if given as a radiosensitizer concurrently with radiation therapy at least 12 weeks prior to registration or if given as part of any adjuvant therapy regimen \> 6 months prior to study enrollment. * Life expectancy of at least 12 weeks (3 months) * For patients who have received prior cryotherapy, radiofrequency ablation, therasphere, ethanol injection, transarterial chemoembolization (TACE) or photodynamic therapy, the following criteria must be met: 28 days have elapsed since that therapy (lesions that have not been treated with local therapy must be present and measureable. * Able to understand and willing to sign the written informed consent form * All acute toxic effects of any prior treatment have resolved to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) v4.0 Grade 1 or less at the time of signing the Informed Consent Form (ICF). * Adequate bone marrow and liver function * Participants can receive 5-FU or capecitabine. * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of study drug. * Men and women of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 3 months after the last dose of study drug. * Able to swallow and retain oral medication Exclusion Criteria: * Previous assignment to treatment during this study. Participants permanently withdrawn from study participation will not be allowed to re-enter study. * Other investigational treatment during or within 21 days before starting study treatment * Child Pugh B and C * Uncontrolled hypertension (systolic pressure \>140 mm Hg or diastolic pressure \> 90 mm Hg \[NCI-CTCAE v4.0\] on repeated measurement) despite optimal medical management * Active or clinically significant cardiac disease * Evidence or history of bleeding diathesis or coagulopathy * Any hemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to start of study medication * Participants with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of informed consent * Active malignancy except for nonmelanoma skin cancer or in situ cervical cancer. Potential participants surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before the trial are allowed. All cancer treatments must be completed at least 3 years prior to study entry (i.e., signature date of the informed consent form). * Potential participants with phaeochromocytoma * Potential participants with severe hepatic impairment (Child-Pugh Class C) * Known history of human immunodeficiency virus (HIV) infection or current chronic or active hepatitis B or C infection requiring treatment with antiviral therapy. * Ongoing infection \> Grade 2 NCI-CTCAE v4.0 * Symptomatic metastatic brain or meningeal tumors * Presence of a non-healing wound, non-healing ulcer, or bone fracture * Renal failure requiring hemo-or peritoneal dialysis * Patients with seizure disorder requiring medication * Persistent proteinuria \>/= Grade 3 NCI-CTCAE v4.0 (\> 3.5 g/24 hours, measured by urine protein:creatinine ratio on a random urine sample) * Interstitial lung disease with ongoing signs and symptoms at the time of informed consent * Pleural effusion or ascites that causes respiratory compromise (≥ NCI-CTCAE version 4.0 Grade 2 dyspnea) * History of organ allograft (including corneal transplant) * Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial * Any malabsorption condition * Women who are pregnant or breast-feeding * Any condition which, in the investigator's opinion, makes the potential participant unsuitable for trial participation * Substance abuse, medical, psychological or social conditions that may interfere with participation in the study or evaluation of the study results