Single-molecule techniques have transformed dramatically the way we think about biophysics, making it possible to address questions about the dynamics of systems in equilibrium that were practically unthinkable just a decade ago. This review focuses on how single-molecule fluorescence and fluorescence correlation techniques have allowed the investigation of the mechanisms by which nucleosomes allow enzymes and other proteins to access DNA regions that are buried within the nucleosome structure. It has been established that DNA-protein and protein-protein interactions in nucleosomes are very dynamic. The dynamics of the interactions between the DNA and the histone proteins have been investigated by single-molecule FRET and fluorescence correlation spectroscopy. Results are consistent with the so-called site exposure model, in which DNA transiently and spontaneously unwraps from the histone core. DNA accessibility is greatest for sites close to the DNA termini, and decreases towards the nucleosome dyad. Evidence also suggests that DNA sequence plays an important role. The dynamics of the H2A-H2B dimers within the nucleosome has also been addressed by several groups in terms of their implications in determining nucleosome stability and DNA dynamics.