The epigenetic inactivation of tumour suppressor genes by promoter CpG island methylation is nowadays one of the hottest topics in cancer research. However, there are still several important open questions: Can we use CpG island hypermethylation to classify tumours according to their clinical behaviour and chemosensitivity? How do we prove that our hypermethylated gene is important for cancer development and/or progression? Which enzymes are directly responsible for the CpG island hypermethylation of tumour suppressor genes? How is the chromatin structure and molecular environment in and around the hypermethylated CpG islands? Can we wake up these dormant hypermethylated tumour suppressor genes in an epigenetic therapy of cancer? Some answers are provided in this review, but other questions remain unsolved, awaiting the eager epigenetic researcher.