KEY INCLUSION CRITERIA:

        Diagnosis of the following:

        Regimen A (FT516 monotherapy):

          -  Primary Refractory AML

          -  Relapsed AML defined as not in CR after 1 or more re-induction attempts; if >60 years
             of age, prior re-induction therapy is not required

        Regimen B (FT516 + rituximab or obinutuzumab):

          -  Histologically documented B-cell lymphoma expected to express CD20 who have relapsed
             after or failed to respond to at least on prior treatment regimen and for whom there
             is no available therapy expected to improve survival.

        All subjects:

          -  Provision of signed and dated informed consent form (ICF)

          -  Age ≥18 years old

          -  Stated willingness to comply with study procedures and duration

          -  Presence of measurable disease

          -  Provision of signed and dated ICF to agree to participate, at time of withdrawal or
             completion of this study, in Fate Therapeutics' long-term follow-up study.

        KEY EXCLUSION CRITERIA:

        All subjects:

          -  Females of reproductive potential who are pregnant or lactating, and males or females
             not willing to use a highly effective form of contraception from Screening through the
             end of the study

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status ≥2

          -  Evidence of insufficient organ function

          -  Receipt of therapy within 2 weeks prior to Cycle 1 Day 1 or within five half-lives,
             whichever is shorter; or any investigational therapy within 28 days prior to Cycle 1
             Day 1

          -  Currently receiving or likely to require systemic immunosuppressive therapy

          -  Prior allogeneic HSCT or allogeneic CAR-T within 6 months of Cycle 1 Day 1, or ongoing
             requirement for systemic graft-versus-host therapy

          -  Receipt of an allograft organ transplant

          -  Known active central nervous system (CNS) involvement by malignancy.

          -  Clinically significant cardiovascular disease

          -  Clinically significant infections including:

          -  Known HIV infection

          -  Known active Hepatitis B (HBV) or Hepatitis C (HCV) infection

          -  Live vaccine <6 weeks prior to start of lympho-conditioning

          -  Known allergy to human albumin and DMSO

          -  QTc >450 msec on screening ECG

        Additional Exclusion Criteria for Regimen A (FT516 monotherapy): Diagnosis of promyelocytic
        leukemia with t(15:17) translocation