Carbon nanotubes are increasingly used in nanomedicine and material chemistry research, mostly because of their small size over a large surface area. Due to their properties, they are very attractive candidates for use in medicine and as drug carriers, contrast agents, biological platforms, and so forth. Carbon nanotubes (CNTs) may affect many organs, directly or indirectly, so there is a need for toxic effects evaluation. The main mechanisms of toxicity include oxidative stress, inflammation, the ability to damage DNA and cell membrane, as well as necrosis and apoptosis. The research concerning CNTs focuses on different animal models, functionalization, ways of administration, concentrations, times of exposure, and a variety of properties, which have a significant effect on toxicity. The impact of pristine CNTs on toxicity in rodent models is being increasingly studied. However, it is immensely difficult to compare obtained results since there are no standardized tests. This review summarizes the toxicity issues of pristine CNTs in rodent models, as they are often the preferred model for human disease studies, in different organ systems, while considering the various factors that affect them. Regardless, the results showed that the majority of toxicological studies using rodent models revealed some toxic effects. Even with different properties, carbon nanotubes were able to generate inflammation, fibrosis, or biochemical changes in different organs. The problem is that there are only a small amount of long-term toxicity studies, which makes it impossible to obtain a good understanding of later effects. This article will give a greater overview of the situation on toxicity in many organs. It will allow researchers to look at the toxicity of carbon nanotubes in a broader context and help to identify studies that are missing to properly assess toxicity.