Hematopoietic stem/progenitor cells (HSPC) and/or non-T effector cells are genetically modified to express (i) an extracellular component including a ligand binding domain that binds a cellular marker preferentially expressed on an unwanted cell; and (ii) an intracellular component comprising an effector domain. Among other uses, the modified cells can be administered to patients to target unwanted cancer cells without the need for immunological matching before administration.