In this review, we summarize —from a materials science perspective— the current state of the field of polymer conjugates of peptide and protein drugs, with a focus on polymers that have been developed as alternatives to the current gold standard, poly(ethylene glycol) (PEG). PEGylation, or the covalent conjugation of PEG to biological therapeutics to improve their therapeutic efficacy by increasing their circulation half-lives and stability, has been the gold standard in the pharmaceutical industry for several decades. After years of research and development, the limitations of PEG, specifically its non-degradability and immunogenicity have become increasingly apparent. While PEG is still currently the best polymer available with the longest clinical track record, extensive research is underway to develop alternative materials in an effort to address these limitations of PEG. Many of these alternative materials have shown promise, though most of them are still in an early stage of development and their in vivo distribution, mechanism of degradation, route of elimination and immunogenicity have not been investigated to a similar extent as for PEG. Thus, further in-depth in vivo testing is essential to validate whether any of the alternative materials discussed in this review qualify as a replacement for PEG.