Poly(ethylene terephthalate) (PET) is one of the polymers most widely used in the packaging industry. However, it is highly desirable to enhance its barrier properties for applications, such as carbonated drinks and other rigid and flexible packaging applications. The nanocomposites route offers unique possibilities to enhance the properties of this material, provided that adequate thermally resistant and legislation complying nanoadditives are used. This study presents novel PET nanocomposites with enhanced barrier properties to oxygen, water, and limonene based on a new specifically developed food-contact-complying highly swollen montmorillonite grade, and, furthermore, presents and discusses morphological data. Moreover, given the current interest in the packaging industry to replace this material by other biopolyesters, a comparative barrier performance of PET nanocomposites versus that of biopolymers, such as poly(lactic acid) (PLA), polyhydroxyalkanoates (PHB, PHBV), and polycaprolactones (PCL) and their corresponding nanocomposites is also reported.