The majority of therapies that target individual proteins rely on specific activity-modulating interactions with the target protein—for example, enzyme inhibition or ligand blocking. However, several major classes of therapeutically relevant proteins have unknown or inaccessible activity profiles and so cannot be targeted by such strategies. Protein-degradation platforms such as proteolysis-targeting chimaeras (PROTACs)^, and others (for example, dTAGs, Trim-Away, chaperone-mediated autophagy targeting and SNIPERs) have been developed for proteins that are typically difficult to target; however, these methods involve the manipulation of intracellular protein degradation machinery and are therefore fundamentally limited to proteins that contain cytosolic domains to which ligands can bind and recruit the requisite cellular components. Extracellular and membrane-associated proteins—the products of 40% of all protein-encoding genes—are key agents in cancer, ageing-related diseases and autoimmune disorders, and so a general strategy to selectively degrade these proteins has the potential to improve human health. Here we establish the targeted degradation of extracellular and membrane-associated proteins using conjugates that bind both a cell-surface lysosome-shuttling receptor and the extracellular domain of a target protein. These initial lysosome-targeting chimaeras, which we term LYTACs, consist of a small molecule or antibody fused to chemically synthesized glycopeptide ligands that are agonists of the cation-independent mannose-6-phosphate receptor (CI-M6PR). We use LYTACs to develop a CRISPR interference screen that reveals the biochemical pathway for CI-M6PR-mediated cargo internalization in cell lines, and uncover the exocyst complex as a previously unidentified—but essential—component of this pathway. We demonstrate the scope of this platform through the degradation of therapeutically relevant proteins, including apolipoprotein E4, epidermal growth factor receptor, CD71 and programmed death-ligand 1. Our results establish a modular strategy for directing secreted and membrane proteins for lysosomal degradation, with broad implications for biochemical research and for therapeutics.