The comet assay (single-cell gel electrophoresis) is a simple, cost-efficient, robust, reliable, and user-friendly method for measuring DNA damage. The in vitro comet assay can be applied in advanced in vitro mini-organ and mini-tissue models. Higher-throughput formats of the assay, such as 48/96 mini-gels on GelBond® film, and the 12-mini-gel slide format, in combination with automated scoring, make the comet assay a valuable screening method for the genotoxic potential of chemicals. In compliance with the 3Rs to reduce, refine, and replace animal experiments, the development of new approach methods (NAMs) is an important part of the paradigm shift in toxicology toward Next Generation Risk Assessment (NGRA), based on non-animal hazard identification and characterization of chemicals. In the case of advanced cell models, the cells are often grown in three-dimensional (3D) culture, and multiple cell types representative of different organs can be co-cultivated. We demonstrate the applicability of the comet assay with commonly applied advanced models from liver, lung, breast, gut, skin, and brain. We describe both the in vitro standard alkaline version of the comet assay (ACA) which measures DNA strand breaks, and the enzyme-linked modification (ELCA) that allows detection of specific base alterations by applying lesion-specific endonucleases (e.g., formamidopyrimidine-DNA glycosylase (Fpg) and endonuclease III (Endo III) for oxidized purines and pyrimidines, respectively). We consider basic methodological issues, experimental design including treatment conditions, and the importance of including cytotoxicity testing—all of which could have an impact on and/or give biased results. Protocols are provided for both the standard 2-gel and 12-gel slide formats. Further, we address critical points that need to be taken into consideration when assessing genotoxicity. The adaptation of the comet assay to advanced models such as 3D cell cultures, co-cultures, and air-liquid interface (ALI) exposure systems marks a significant advance in genotoxicity testing. These models offer more biologically relevant contexts for measuring DNA damage and repair, leading to better risk assessment and the development of safer chemicals, such as pharmaceuticals, cosmetics, food additives, as well as influencing environmental policies.