Inclusion Criteria:

          -  Histologically or cytologically confirmed diagnosis of the following malignancies:
             CP-CML, blast phase chronic myeloid leukemia (BP-CML), accelerated phase chronic
             myeloid leukemia (AP-CML); acute lymphoblastic leukemia/acute lymphocytic leukemia
             (ALL); acute myeloid leukemia (AML); other leukemias; lymphoma; any other tumors,
             including tumors of the central nervous system (CNS), for which standard therapy is
             not available or is not indicated

          -  Phase 1:

               -  Participants with CML who are resistant to or intolerant to at least 1 prior
                  BCR-ABL-targeted TKI therapy.

               -  Participants with ALL who have failed all available or indicated therapies, which
                  may have included 1 prior BCR-ABL-targeted TKI therapy.

               -  Participants with AML or other leukemias who have failed at least 1 prior
                  induction attempt or for whom no effective standard therapy is available or
                  indicated.

               -  Participants with solid tumors (including tumors of the CNS) or lymphomas who
                  have progressed despite standard therapy or for whom no effective standard
                  therapy is available or indicated.

          -  Phase 2 (CP-CML): Participants who are resistant to or intolerant of at least 1 prior
             BCR-ABL-targeted TKI therapy or have the T315I kinase domain mutation.

          -  Phase 2 (other leukemias or solid tumors):

               -  Participants with ALL who have failed all available or indicated therapies, which
                  must have included 1 prior BCR-ABL-targeted TKI therapy.

               -  Participants with AML or other leukemias who have failed at least 1 prior
                  induction attempt or for whom no effective standard therapy is available or
                  indicated.

               -  Participants with solid tumors (including tumors of the CNS) with mutation of
                  RET, KIT, FGFR, PDGFR, VEGFR or any other mutations where ponatinib may have
                  biological activity or lymphomas who progressed despite standard therapy or for
                  whom no effective standard therapy is available or indicated.

          -  Karnofsky performance status ≥ 40% for participants > 16 years old or Lansky Play
             Scale ≥ 40 for pediatric participants ≤ 16 years old.

          -  Must have recovered to < Grade 2 per the NCI CTCAE v5.0 or to baseline from any
             non-hematologic toxicities (except alopecia) due to previous therapy.

          -  Willingness to avoid pregnancy or fathering children.

        Exclusion Criteria:

          -  Participants with CP-CML who are in MCyR or better.

          -  Prior therapies:

               -  Participants with BP-CML, ALL, or AML who have received corticosteroids or
                  hydroxyurea within 24 hours before the first dose of ponatinib; vincristine
                  within 7 days before the first dose of ponatinib; or other chemotherapy
                  (excluding intrathecal chemotherapy) within 14 days before the first dose of
                  ponatinib

               -  Participants (except the BP-CML, ALL, and AML participants described above) who
                  have had cytotoxic chemotherapy or radiotherapy within 21 days (or 42 days for
                  nitrosoureas or mitomycin C) before the first dose of ponatinib.

               -  Prior radiation therapy within 6 weeks or radio-isotope therapy within 6 weeks
                  before the first dose of ponatinib.

               -  Autologous or allogeneic stem cell transplant < 3 months before the first dose of
                  ponatinib.

               -  Prior treatment with any of the following: immunosuppressive therapy (including
                  post stem cell transplant regimens) within 14 days before the first dose of
                  ponatinib; any targeted cancer therapy (including TKIs) within 7 days before the
                  first dose of ponatinib; any other investigational anticancer agents within 30
                  days or 5 half-lives, whichever is longer, before randomization; any monoclonal
                  antibody-directed anticancer therapy within 5 half-lives of the first dose of
                  ponatinib; any chimeric antigen receptor therapy within 28 days before the first
                  dose of ponatinib; ponatinib.

          -  Laboratory values at screening outside the protocol-defined ranges.

          -  Significant concurrent, uncontrolled medical condition, including but not limited to
             protocol-defined pancreatic, cardiac, cerebral, coagulation, gastrointestinal, and
             genetic conditions.

          -  Any active ≥ Grade 2 graft-versus-host disease.

          -  Chronic or current active uncontrolled infectious disease requiring systemic
             antibiotics, antifungal, or antiviral treatment.

          -  Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection that requires
             treatment or at risk for HBV reactivation.

          -  Known HIV infection.

          -  Known hypersensitivity or severe reaction to ponatinib or excipients of ponatinib.

          -  Receipt of live (including attenuated) vaccines or anticipation of need for such
             vaccines during the study.

          -  Females who are pregnant or lactating.