Epigenetic abnormalities are extremely widespread in cancer. Some of them are mere consequences of transformation, but some actively contribute to cancer initiation and progression; they provide powerful new biological markers, as well as new targets for therapies. In this review, we examine the recent literature and focus on one particular aspect of epigenome deregulation: large-scale chromatin changes, causing global changes of DNA methylation or histone modifications. After a brief overview of the one-dimension (1D) and three-dimension (3D) epigenome in healthy cells and of its homeostasis mechanisms, we use selected examples to describe how many different events (mutations, changes in metabolism, and infections) can cause profound changes to the epigenome and fuel cancer. We then present the consequences for therapies and briefly discuss the role of single-cell approaches for the future progress of the field.