Lifson - Poland - Scheraga Models of DNA

DNA is one of the most investigated systems in science not only for its basic relevance for biology, but also because it exhibits very interesting features associated with its structure and dynamics. These aspects have attracted from the very beginning the interest of physicists, chemists and mathematicians. In particular, much progress has been done during the decades on the understanding of the mechanism of denaturation dynamics in the double-strand of DNA in the presence of structural and topological disorder. We report here the introductory remarks to the seminars, that were presented on this topic in occasion of the conference on "Inhomogeneous Random Systems", held at the Institute Henri Poincare on the 25th of January 2012.