Provided herein are compositions and methods relating to cell-penetrating conjugates for the delivery of therapeutic polypeptides or polynucleotides to cells or tissues of the body. The delivery conjugate comprises a cell-penetrating peptide and a nuclear localization signal sequence plus an effector moiety (such as a polypeptide or polynucleotide) as the payload, optionally further including an epitope tag as well as a solubility peptide and a configurating peptide. The delivery conjugate can also include a component capable of specifically directing the conjugate to a target cell or tissue, making the conjugate effective for treating diseases in the target tissue.