There is growing evidence that cancer chemoprevention employing natural, bioactive compounds may halt or at least slow down the different stages of carcinogenesis. A particularly advantageous effect is attributed to derivatives of sulfur-organic phytochemicals, such as glucosinolates (GLs) synthesized mainly in Brassicaceae plant family. GLs are hydrolysed enzymatically to bioactive isothiocyanates (ITC) and indoles, which exhibit strong anti-inflammatory and anti-carcinogenic activity. Highly bioavailable electrophilic ITC are of particular interest, as they can react with nucleophilic groups of important biomolecules to form dithiocarbamates, thiocarbamates and thioureas. These modifications seem responsible for chemopreventive activity, but also for genotoxicity and mutagenicity. It was documented that ITC can permanently bind to important biomolecules such as glutathione, cytoskeleton proteins, transcription factors NF-κB and Nrf2, thiol-disulfide oxidoreductases, proteasome proteins or heat shock proteins. Furthermore, ITC may also affect epigenetic regulation of gene expression, e.g. by inhibition of histone deacetylases. Some other derivatives of glucosinolates, especially indoles, are able to form covalent bonds with nucleobases in DNA, which may result in genotoxicity and mutagenicity. This article summarizes the current state of knowledge about glucosinolates and their degradation products in terms of possible interactions with reactive groups of cellular molecules.