At the cellular level, cancer is the disease of both the genome and the epigenome, and the interplay between genetic mutations and epigenetic states may occur at the level of elementary chromatin units, the nucleosomes. They are formed by a segment of DNA wrapped around an octamer of histone proteins. In this review, we survey various mechanisms of cancer etiology and progression mediated by histones and nucleosomes. In particular, we discuss the effects of mutations in histones, changes in their expression and slicing on epigenetic dysregulation and carcinogenesis. The links between cancer phenotypes and differential expression of histone variants and isoforms are summarized. Finally, we discourse the geometric and steric effects of DNA compaction in nucleosomes on DNA mutation rate, interactions with transcription factors, including pioneer transcription factors, and prospects of cancer cells' genome and epigenome editing.