The zero (0-D) and one-dimensional (1-D) carbon nanomaterials have gained attention among researchers because they exhibit a larger surface area to volume ratio, and a smaller size. Furthermore, carbon is ubiquitously present in all living organisms. However, toxicity is a major concern while utilizing carbon nanomaterials for biomedical applications such as drug delivery, biosensing, and tissue regeneration. In the present review, we have summarized some of the recent findings of cellular and animal level toxicity studies of 0-D (carbon quantum dot, graphene quantum dot, nanodiamond, and carbon black) and 1-D (single-walled and multi-walled carbon nanotubes) carbon nanomaterials. The in vitro toxicity of carbon nanomaterials was exemplified in normal and cancer cell lines including fibroblasts, osteoblasts, macrophages, epithelial and endothelial cells of different sources. Similarly, the in vivo studies were illustrated in several animal species such as rats, mice, zebrafish, planktons and, guinea pigs, at various concentrations, route of administrations and exposure of nanoparticles. In addition, we have described the unique properties and commercial usage, as well as the similarities and differences among the nanoparticles. The aim of the current review is not only to signify the importance of studying the toxicity of 0-D and 1-D carbon nanomaterials, but also to emphasize the perspectives, future challenges and possible directions in the field.