Knowing the mutagenic and carcinogenic properties of chemicals is very important for their hazard (and risk) assessment. One of the crucial events that trigger genotoxic and sometimes carcinogenic effects is the forming of adducts between chemical compounds and nucleic acids and histones. This review takes a look at the mechanisms related to specific functional groups (structural alerts or toxicophores) that may trigger genotoxic or epigenetic effects in the cells. We present up-to-date information about defined structural alerts with their mechanisms and the software based on this knowledge (QSAR models and classification schemes).