Inclusion Criteria:

          -  Patients with histologically or cytologically confirmed unresectable, locally advanced
             hepatocellular carcinoma as defined by Barcelona Clinic Liver Cancer (BCLC) (B)
             intermediate stage or BCLC (C) advanced stage without extra-hepatic disease (only with
             branch portal vein thrombosis)

          -  Capable of giving signed informed consent which includes compliance with the
             requirements and restrictions listed in the informed consent form (ICF) and in this
             protocol. Written informed consent and any locally required authorization (e.g.,
             Health Insurance Portability and Accountability Act in the United States [US])
             obtained from the patient/legal representative prior to performing any
             protocol-related procedures, including screening evaluations

          -  Patient is willing and able to comply with the protocol for the duration of the study
             including undergoing treatment and scheduled visits and examinations including follow
             up

          -  Eastern Cooperative Oncology Group (ECOG) 0-1

          -  Must have a life expectancy of at least 12 weeks

          -  Evidence of post-menopausal status or negative urinary or serum pregnancy test for
             female pre-menopausal patients. Women will be considered post-menopausal if they have
             been amenorrheic for 12 months without an alternative medical cause. The following
             age-specific requirements apply:

               -  Women < 50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and if they have luteinizing hormone and follicle-stimulating hormone
                  levels in the post-menopausal range for the institution or underwent surgical
                  sterilization (bilateral oophorectomy or hysterectomy)

               -  Women >= 50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of all exogenous hormonal
                  treatments, had radiation-induced menopause with last menses > 1 year ago, had
                  chemotherapy-induced menopause with last menses > 1 year ago, or underwent
                  surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or
                  hysterectomy)

          -  Male patients must be surgically sterile, or if sexually active and having a
             pre-menopausal female partner then must be using an acceptable form of contraception

          -  Have a Child-Pugh class A liver score within 7 days of radioembolization

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded) as
             outlined in RECIST version 1.1

          -  Patients should have been identified by their respective physicians as candidates for
             radioembolization

          -  Body weight > 30 kg

          -  Subjects with chronic infection by hepatitis C virus (HCV) who are untreated are
             allowed on study. In addition, subjects with successful HCV treatment (defined as
             sustained virologic response [SVR] 12 or SVR 24) are allowed as long as 4 weeks have
             passed between completion of HCV therapy and start of study drug

          -  Subjects with hepatitis B virus (HBV) may only be enrolled if their hepatitis is
             judged clinically stable by the investigator

          -  Hemoglobin >= 9.0 g/dL

          -  Absolute neutrophil count (ANC) >= 1500/uL

          -  Platelet count >= 75000/uL

          -  Total bilirubin < 2.0 mg/dL. This will not apply to patients with confirmed Gilbert's
             syndrome (persistent or recurrent hyperbilirubinemia that is predominantly
             unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed
             only in consultation with their physician

          -  Aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT/serum glutamate pyruvate transaminase [SGPT]) =< 5 x
             upper limit of normal (ULN)

          -  Albumin >= 2.8 g/dL

          -  International normalized ration =< 1.6

          -  Measured creatinine clearance (CL) > 40 mL/min or calculated creatinine CL > 40 mL/min
             by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine
             collection for determination of creatinine clearance

        Exclusion Criteria:

          -  Portal vein invasion at the main portal branch (Vp4), inferior vena cava, or cardiac
             involvement of hepatocellular carcinoma (HCC) based on imaging. Vascular invasion to
             portal vein side branches are eligible for study

          -  Evidence of diffuse HCC (tumor burden occupying > 50% of liver)

          -  Any evidence of known metastatic disease

          -  Major surgical procedure (as defined by the investigator) within 28 days prior to
             radioembolization

               -  Note: Local surgery of isolated lesions for palliative intent is acceptable

          -  Participation in another clinical study with an investigational product during the
             last 4 weeks

          -  Concurrent enrollment in another clinical study, unless it is an observational
             (non-interventional) clinical study or during the follow-up period of an
             interventional study

          -  Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapy, endocrine
             therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal
             antibodies) =< 28 days prior to the first dose of study drug. If sufficient wash-out
             time has not occurred due to the schedule or pharmacokinetic (PK) properties of an
             agent, a longer wash-out period will be required, as agreed by AstraZeneca/MedImmune
             and the investigator

          -  Prior exposure to anti-PD-1/PD-L1 inhibitor or anti-CTLA4 inhibitor, including
             durvalumab or tremelimumab

          -  Any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria
             for Adverse Events (CTCAE) grade >= 2 from previous anticancer therapy with the
             exception of alopecia, vitiligo, and the laboratory values defined in the inclusion
             criteria

          -  Patients with grade >= 2 neuropathy will be evaluated on a case-by-case basis after
             consultation with the study physician

          -  Patients with irreversible toxicity not reasonably expected to be exacerbated by
             treatment with durvalumab and/or tremelimumab may be included only after consultation
             with the study physician

          -  Active or prior documented autoimmune or inflammatory disorders (including
             inflammatory bowel disease [e.g., colitis or Crohn's disease], diverticulitis [with
             the exception of diverticulosis], systemic lupus erythematosus, Sarcoidosis syndrome,
             or Wegener syndrome [granulomatosis with polyangiitis, Graves' disease, rheumatoid
             arthritis, hypophysitis, uveitis, etc]). The following are exceptions to this
             criterion:

               -  Patients with vitiligo or alopecia

               -  Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on
                  hormone replacement

               -  Any chronic skin condition that does not require systemic therapy

               -  Patients without active disease in the last 5 years may be included but only
                  after consultation with the study physician

               -  Patients with celiac disease controlled by diet alone

          -  History of allogenic organ transplantation

          -  Evidence of pulmonary lung shunt greater than 10% or expected lung dose of > 30 Gy

          -  Uncontrolled intercurrent illness, including but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable
             angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic
             gastrointestinal conditions associated with diarrhea, or psychiatric illness/social
             situations that would limit compliance with study requirement, substantially increase
             risk of incurring adverse events (AEs) or compromise the ability of the patient to
             give written informed consent

          -  History of another primary malignancy except for

               -  Malignancy treated with curative intent and with no known active disease >= 5
                  years before the first dose of study treatment and of low potential risk for
                  recurrence

               -  Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease

               -  Adequately treated carcinoma in situ without evidence of disease

          -  History of active primary immunodeficiency

          -  Receipt of live attenuated vaccine within 30 days prior to the first dose of study
             treatment

               -  Note: Patients, if enrolled, should not receive live vaccine whilst receiving
                  study treatment and up to 30 days after the last dose of study treatment

          -  Active systemic infection including tuberculosis (clinical evaluation that includes
             clinical history, physical examination and radiographic findings, and tuberculosis
             (TB) testing in line with local practice. Use of antibiotics to treat superficial
             infection or contamination of tumor shall not, by itself, be considered evidence of
             infection

          -  History of leptomeningeal carcinomatosis

          -  Known allergy or hypersensitivity to any of the study drugs or any of the study drug
             excipients

          -  Any concurrent chemotherapy, investigational product (IP), biologic, or hormonal
             therapy for cancer treatment. Concurrent use of hormonal therapy for
             non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable

          -  Current or prior use of immunosuppressive medication within 14 days before the first
             dose of durvalumab or tremelimumab. The following are exceptions to this criterion:

               -  Intranasal, inhaled, topical steroid or local steroid injections (e.g., intra
                  articular injection)

               -  Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of
                  prednisone or its equivalent

               -  Steroids as premedication for hypersensitivity reactions (e.g., computed
                  tomography [CT] scan premedication)

          -  Female patients who are pregnant or breastfeeding or male or female patients of
             reproductive potential who are not willing to employ effective birth control from
             screening to 90 days after the last dose of durvalumab + tremelimumab combination
             therapy or 90 days after the last dose of durvalumab monotherapy, whichever is longer

          -  Female subjects, unless postmenopausal or surgically sterile, unwillingness to
             practice effective contraception, as per investigator discretion during the study. The
             rhythm method is not to be used as the sole method of contraception

          -  Male subjects, unwillingness to practice effective contraception (per investigator
             discretion) while taking part in this study, because the effects of the SIR-Spheres
             treatment on sperm or upon the development of an unborn child are unknown

          -  Inability or unwillingness to understand or sign a written informed consent document

          -  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)