Changes in the genetic material can lead to serious human health defects, as mutations in somatic cells may cause cancer and can contribute to other chronic diseases. Genotoxic events can appear at both the DNA, chromosomal or (during mitosis) whole genome level. The study of mechanisms leading to genotoxicity is crucially important, as well as the detection of potentially genotoxic compounds. We consider the current state of the art and describe here the main endpoints applied in standard human in vitro models as well as new advanced 3D models that are closer to the in vivo situation. We performed a literature review of in vitro studies published from 2000–2020 (August) dedicated to the genotoxicity of nanomaterials (NMs) in new models. Methods suitable for detection of genotoxicity of NMs will be presented with a focus on advances in miniaturization, organ-on-a-chip and high throughput methods.