Genotoxicity and carcinogenicity assessment is an essential part of the human health safety assessment of all types of substances, including pharmaceuticals, industrial chemicals, pesticides, food additives, cosmetics ingredients. The possibility to predict with a sufficient degree of reliability, the genotoxicity and/or carcinogenicity potential of a chemical by means of in silico quantitative approaches is a topic of high interest for health prevention strategies and regulatory frameworks. In Europe, the safety evaluation of cosmetics is based on the evaluation of each individual ingredient. The marketing of cosmetic products experimentally tested on animals is actually completely banned in the EU and an increasing number of countries is now following this ban as well. This means that the cosmetic industry has an urgent need for alternative approaches for the safety assessment of ingredients of consumer products. In recent decades, much attention has been given to the use and further development of innovative non testing strategies based on categories, grouping, Read-Across and (Quantitative) Structure-Activity Relationships ((Q)SARs), to be used in isolation or in combination with in vitro assays. This paper presents an overview of the most important in silico approaches for prediction of genotoxicity and carcinogenicity, regulatory initiatives and frameworks with a special emphasis on cosmetics. © 2019 Elsevier B.V.