The field of biorenewable polymers is ever-expanding, aided by the interest of the general public to adopt more sustainable practices for natural resource utilization as well as waste generation. This review summarizes recent efforts to synthesize biobased thermoplastics with glass transition temperature (Tg) values exceeding that of polylactic acid (PLA), near 55 °C. A high Tg is essential for materials that aspire to replace any incumbent commodity plastics employed in the amorphous state. The first section focuses on commercial bioplastics and describes: approaches toward biorenewable polyethylene terephthalate (PET); efforts to improve the Tg of PLA; and advances toward polyethylene furanoate (PEF). The remaining sections catalogue a wide variety of novel, high Tg bioplastics categorized as: aromatic biopolymers, carbocyclic and heterocyclic biopolymers, and vinyl-type biopolymers synthesized via radical polymerization.