  As a key molecule of Life, Deoxyribonucleic acid (DNA) is the focus of
numbers of investigations with the help of biological, chemical and physical
techniques. From a physical point of view, both experimental and theoretical
works have brought quantitative insights into DNA base-pairing dynamics that we
review in this Report, putting emphasis on theoretical developments. We discuss
the dynamics at the base-pair scale and its pivotal coupling with the polymer
one, with a polymerization index running from a few nucleotides to tens of
kilo-bases. This includes opening and closure of short hairpins and oligomers
as well as zipping and unwinding of long macromolecules. We review how
different physical mechanisms are either used by Nature or utilized in
biotechnological processes to separate the two intertwined DNA strands, by
insisting on quantitative results. They go from thermally-assisted denaturation
bubble nucleation to force- or torque- driven mechanisms. We show that the
helical character of the molecule, possibly supercoiled, can play a key role in
many denaturation and renaturation processes. We categorize the mechanisms
according to the relative timescales associated with base-pairing and chain
degrees of freedom such as bending and torsional elastic ones. In some specific
situations, these chain degrees of freedom can be integrated out, and the
quasi- static approximation is valid. The complex dynamics then reduces to the
diffusion in a low-dimensional free-energy landscape. In contrast, some
important cases of experimental interest necessarily appeal to
far-from-equilibrium statistical mechanics and hydrodynamics.
