a Schematic of a conventional CAR (high-affinity CAR) typically containing a high-affinity antigen-binding domain (usually a single-chain variable fragment, scFv) fused via a dimerizing hinge region (derived from, e.g., CD8α) to the cytoplasmic domains of a co-stimulatory receptor (mostly 4-1BB or CD28) and CD3ζ. Due to high-affinity binding, monovalent interaction with the target antigen is sufficient for CAR activation. b Schematic of a low-affinity CAR in which a low-affinity antigen-binding domain is fused to the same conventional CAR backbone shown in (a). We hypothesized that such low-affinity CARs require bivalent interaction with the antigen for efficient activation. We further hypothesized that this avidity-based concept (i.e., the dependency on bivalent antigen recognition) can be exploited for various applications: c for generating ON-switch AvidCARs whose function is regulated by a dimerizing small molecule; d for constructing AND-gate AvidCARs which are dimerized by a soluble antigen B, leading to avidity-based recognition of antigen A; e, f and for the design of heterodimeric AND-gate AvidCARs specifically recognizing a combination of two surface bound antigens with two different recognition domains, respectively. This AND-gate concept can be realized in a nonswitchable format by constitutive CAR heterodimerization (e) or in a switchable version by inducing heterodimerization with a small molecule (f).