Poly(alkylene terephthalate)s, PET and PBT in particular, are materials of great relevance and growing projection in the thermoplastic field but are today almost totally produced from fossil resources. The current huge consumption of these polyesters necessitates urgent actions addressed to make them renewable by using naturally-occurring raw materials. Among the different approaches that are being followed to develop bio-based poly(terephthalate)s, the use of bicyclic carbohydrate-derived difunctional compounds as building-blocks is receiving much attention in the last few years because partially renewable polyesters with high Tg may be thus obtained. This review presents a critical account of the terephthalate homopolymers and copolymers that have been synthesized using the two types of carbohydrate-based bicyclic monomers, isohexides and diacetals, explored to date. The properties displayed by the novel bio-based poly(terephthalate)s in relation to the bicyclic structure of the used monomers are comparatively reviewed and their potential as emergent materials for thermoplastic applications is evaluated.