Common sugar alcohols used as artificial sweeteners and components of polymer networks represent low molecular weight polyhydroxymethylenes (PHMs) with the general formula [CH(OH)]n H2 but very low degree of polymerization (n = 2–6). Herein high molecular weight PHM (n >> 100) unparalleled in nature is tailored for 3D printing and medical applications by free radical polymerization of 1,3‐dioxol‐2‐one vinylene carbonate to produce polyvinylene carbonate (PVCA) which yields PHM by hydrolysis. Furthermore, PVCA is solution processable and enables PHM functionalization, membrane formation, and extrusion‐based 3D printing. Opposite to cellulose, amorphous PHM is plasticized by water and is readily functionalized via PVCA aminolysis/hydrolysis to produce polyhydroxymethylene urethane (PHMU), enable PHM crosslinking and coupling of PHM with amine‐functional components like gelatin. After hydrolysis/aminolysis the original PVCA shapes are retained. PVCA solution casting yields PVCA and PHM which exhibits uniform and hierarchic pore architectures. Asymmetric membranes, hydrogels, PHM/collagen blends, and electrospun nonwovens of PVCA, PHM, and PHMU are readily tailored for medical applications. 3D printing of PVCA dispersions containing hydroxyapatite affords porous PVCA, PHMU, and PHM scaffolds useful in regenerative medicine. PHM and functionalized PHMs as carbohydrate‐inspired multifunctional materials indicate in vitro biocompatibility and hold great promise for applications in medicine and health care.