Staudinger established a century ago the existence of covalent macromolecules, work that led to the development of transformative materials of great benefit to society and a "quantum leap" in our understanding of biological systems. Over the past few decades the concept of supramolecular polymers has emerged-chemical systems in which structural units bond strongly to each other non-covalently. These dynamic systems actually exist in the natural world and can create soft materials with structures, properties, and functions beyond the ones we know in Staudinger polymers. We reflect here on the potential of novel systems in which covalent and supramolecular polymers are chemically integrated and describe them as hybrid bonding polymers. This paper describes the concept with recent examples from the Stupp laboratory, and discusses their potential functions as robotic materials that mimic living matter and structures that offer new ideas on how to recycle and reuse soft materials.