One-dimensional (1D) carbon nanotubes (CNTs) and the two-dimensional (2D) graphene represent the most widely studied allotropes of carbon. Due to their unique structural, electrical, mechanical and optical properties, 1D and 2D carbon nanostructures are considered to be leading candidates for numerous applications in biomedical fields, including tissue engineering, drug delivery, bioimaging and biosensors. The biocompatibility and toxicity issues associated with these nanostructures have been a critical impediment for their use in biomedical applications. In this review, we present an overview of the various materials types, properties, functionalization strategies and characterization methods of 1D and 2D carbon nanomaterials and their derivatives in terms of their biomedical applications. In addition, we discuss various factors and mechanisms affecting their toxicity and biocompatibility.