About three quarter of all eukaryotic DNA is wrapped around protein cylinders, forming nucleosomes. Even though the histone proteins that make up the core of nucleosomes are highly conserved in evolution, nucleosomes can be very different from each other due to posttranslational modifications of the histones. Another crucial factor in making nucleosomes unique has so far been underappreciated: the sequence of their DNA. This review provides an overview of the experimental and theoretical progress that increasingly points to the importance of the nucleosomal base pair sequence. Specifically, we discuss the role of the underlying base pair sequence in nucleosome positioning, sliding, breathing, force-induced unwrapping, dissociation and partial assembly and also how the sequence can influence higher-order structures. A new view emerges: the physical properties of nucleosomes, especially their dynamical properties, are determined to a large extent by the mechanical properties of their DNA, which in turn depends on DNA sequence.