Chimeric antigen receptor (CAR) engineered T cell therapies individually prepared for each patient with autologous T cells have recently changed clinical practice in the management of B cell malignancies. Even though CARs used to redirect polyclonal T cells to the tumor are not HLA restricted, CAR T cells are also characterized by their endogenous T cell receptor (TCR) repertoire. Tumor-antigen targeted TCR-based T cell therapies in clinical trials are thus far using "conventional" αβ-TCRs that recognize antigens presented as peptides in the context of the major histocompatibility complex. Thus, both CAR- and TCR-based adoptive T cell therapies (ACTs) are dictated by compatibility of the highly polymorphic HLA molecules between donors and recipients in order to avoid graft-versus-host disease and rejection. The development of third-party healthy donor derived well-characterized off-the-shelf cell therapy products that are readily available and broadly applicable is an intensive area of research. While genome engineering provides the tools to generate "universal" donor cells that can be redirected to cancers, we will focus our attention on third-party off-the-shelf strategies with T cells that are characterized by unique natural features and do not require genome editing for safe administration. Specifically, we will discuss the use of virus-specific T cells, lipid-restricted (CD1) T cells, MR1-restricted T cells, and γδ-TCR T cells. CD1- and MR1-restricted T cells are not HLA-restricted and have the potential to serve as a unique source of universal TCR sequences to be broadly applicable in TCR-based ACT as their targets are presented by the monomorphic CD1 or MR1 molecules on a wide variety of tumor types. For each cell type, we will summarize the stage of preclinical and clinical development and discuss opportunities and challenges to deliver off-the-shelf targeted cellular therapies against cancer.