Cell-penetrating peptides (CPPs) have long held great promise for the manipulation of living cells for therapeutic and research purposes. They allow a wide array of biomolecules from large, oligomeric proteins to nucleic acids and small molecules to rapidly and efficiently traverse cytoplasmic membranes. With few exceptions, if a molecule can be associated with a CPP, it can be delivered into a cell. However, a growing realization in the field is that CPP-cargo fusions largely remain trapped in endosomes and are eventually targeted for degradation or recycling rather than released into the cytoplasm or trafficked to a desired subcellular destination. This 'endosomal escape problem' has confounded efforts to develop CPP-based delivery methods for drugs, enzymes, plasmids, etc. This review provides a brief history of CPP research and discusses current issues in the field with a primary focus on the endosomal escape problem, for which several promising potential solutions have been developed. Are we on the verge of developing technologies to deliver therapeutics such as siRNA, CRISPR/Cas complexes and others that are currently failing because of an inability to get into cells, or are we just chasing after another promising but unworkable technology? We make the case for optimism.