Nanomaterials (NMs) generally display fascinating physical and chemical properties that are not always present in bulk materials; therefore, any modification to their size, shape, or coating tends to cause significant changes in their chemical/physical and biological characteristics. The dramatic increase in efforts to use NMs renders the risk assessment of their toxicity highly crucial due to the possible health perils of this relatively uncharted territory. The different sizes and shapes of the nanoparticles are known to have an impact on organisms and an important place in clinical applications. The shape of nanoparticles, namely, whether they are rods, wires, or spheres, is a particularly critical parameter to affect cell uptake and site-specific drug delivery, representing a significant factor in determining the potency and magnitude of the effect. This review, therefore, intends to offer a picture of research into the toxicity of different shapes (nanorods, nanowires, and nanospheres) of NMs to in vitro and in vivo models, presenting an in-depth analysis of health risks associated with exposure to such nanostructures and benefits achieved by using certain model organisms in genotoxicity testing. Nanotoxicity experiments use various models and tests, such as cell cultures, cores, shells, and coating materials. This review article also attempts to raise awareness about practical applications of NMs in different shapes in biology, to evaluate their potential genotoxicity, and to suggest approaches to explain underlying mechanisms of their toxicity and genotoxicity depending on nanoparticle shape.