Carbon nanofillers containing biodegradable polymer composites have become an emerging frontier in materials science and engineering because of their potential as environmentally friendly materials in multiple applications, from load-bearing to advanced packaging to biomedical applications. Herein, we present the effect of processing parameters on the final morphology and the resulting properties of the biodegradable polymer composites containing carbon nanotubes (CNTs) or carbon nanofibers (CNFs). Various strategies can be employed to develop such composites; however, the type of morphology, which results during processing, significantly affects the final properties of the obtained composites. Therefore, various processing strategies such as meltblending, additive manufacturing, and electrospinning are critically reviewed, together with the potential applications in load-bearing, tissue engineering, electromagnetic shielding, gas sensing, and packaging. Finally, we discuss the existing challenges and future directions in designing CNTs/CNFs containing biodegradable polymer composites with desired properties.