Inclusion Criteria:

          -  Participants must have histologic or cytology diagnosis of a known immunogenic solid
             tumor, as described for Part 1 Dose Escalation and Part 2 Cohort Expansion:

          -  Part 1 Dose Escalation:

          -  Participants with advanced or metastatic solid tumors that have exhausted standard
             treatment for their incurable disease and for whom there is currently no programmed
             cell death 1 (PD-1)/ programmed cell death-ligand 1 (PD-L1) approved therapy, with
             immunogenic type tumors such as, but not limited to triple negative breast cancer
             (TNBC), ovarian cancer, small cell lung cancer, mesothelioma, and cholangiocarcinoma.

          -  Participants who are refractory to a PD-1/PD-L1 agent, with tumor types such as
             melanoma, NSCLC, platinum-pretreated head and neck cancer, second line bladder and
             RCC.

          -  Part 2A and 2B Cohort Expansion:

          -  2A : TNBC ABBV-368 monotherapy cohorts: Subjects with locally advanced or metastatic
             TNBC that have exhausted standard treatment for their incurable disease.

          -  2B : Head and Neck cohort: Participants with recurrent squamous cell head and neck
             carcinoma that are not candidates for curative treatment with local or systemic
             therapy, or metastatic (disseminated) head and neck squamous cell carcinoma of the
             oral cavity, oropharynx, hypopharynx, and larynx that is considered incurable by local
             therapies.

          -  Part 3A and 3B Imaging Substudy:

          -  3A: Participants with locally advanced or metastatic TNBC that have exhausted standard
             treatment for their incurable disease and are treatment naïve to a PD-1/PD-L1
             targeting agent.

          -  3B: Participants with recurrent HNSCC that are not candidates for curative treatment
             with local or systemic therapy, or metastatic HNSCC of the oral cavity, oropharynx,
             hypopharynx, and larynx that is considered incurable by local therapies. Participants
             must be treatment naïve to a PD-1/PD-L1 targeting agent.

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0 to 2.

          -  Participants must have immune-related Response Evaluation Criteria for Solid Tumors
             (iRECIST) evaluable or measurable disease in the PART 1 and measurable disease per
             iRECIST in PART 2

          -  Adequate bone marrow, kidney and liver function.

        Exclusion Criteria:

          -  Received anticancer therapy including chemotherapy, immunotherapy, radiation therapy,
             biologic, herbal therapy, or any investigational therapy within a period of 21 days
             prior to the first dose of ABBV-368.

          -  Prior treatment with an OX40 targeting agent.

          -  has known uncontrolled metastases to the central nervous system (CNS).

          -  History of active autoimmune disorders and other conditions that compromise or impair
             the immune system.

          -  Confirmed positive test results for human immunodeficiency virus (HIV), or subjects
             with chronic or active hepatitis A, B or C. Subjects who have a history of hepatitis B
             or C who have documented cures after anti-viral therapy may be enrolled.

          -  Has received live vaccine within 28 days prior to the first dose of study drug.