This dissertation presents a process for directly imprinting or embossing extruded polymers as an advancement in roll-to-roll (R2R) embossing methods that avoids the problems of converting preformed films, increases throughput, and reduces costs. A proof-of-concept R2R apparatus was designed and constructed for directly embossing extruded polymer, and experimental results were evaluated. This laboratory scale R2R apparatus employed a thin metal ribbon belt mold with micro or nano scale features in a calendering setup, with a close coupled induction heating (IH) coil to preheat the ribbon mold above glass transition temperature (Tg) of the polymer, prior to contact with the extrudate at the nip of the calender. This allowed the melted polymer to fully fill the mold patterns before starting to solidify. The thin ribbon mold rapidly conducted heat to the calender roller, providing an effective cooling stage. Microscale and nanoscale features were imprinted directly onto extruded polymer film at a rate of 10 to 12 meters per second, three to over one hundred times the throughput of current R2R processes and orders of magnitude faster than planar processes. Metal ribbon mold belts with nano features were needed to test the direct embossing of extruded polymers at the nano scale. Three different avenues were taken to make such ribbon belts. First, preset nickel alloy molds were obtained. A master mold of the Book of Leviticus with letters 6 µm in width, 6 to 9 µm tall and 60-170 nm high and a nickel alloy DVD master mold with track pitch of 740 nm and 105 nm deep Pits between 400 nm and 1900 nm long. These were welded into stainless steel ribbon belts to form belt molds. Second, a process was developed using base forms or mandrels for metal-forming nickel ribbon belt molds with test patterns that included gratings from 70 to 500 nm and pillars having diameters of 1 µm, 700 nm, 500 nm and 350 nm. Third, an investigation of metal glass (MG) as a candidate mold material was undertaken and a laboratory scale mechanism was designed and constructed to emboss metal glass surfaced rollers thermally.