When quarks and gluons tend to form a dense medium, like in high energy or/and heavy-ion collisions, it is interesting to ask the question which are the relevant degrees of freedom that Quantum Chromodynamics predicts. The present notes correspond to two lectures given at Zakopane in the (rainy) summer of 2006, where this question is adressed concretely in two cases, one in the QCD regime of weak coupling, the other one at strong coupling. (The second Lecture is published on page 3525 of this volume.) Each case corresponds to the study of an elusive but dynamically important transient phase of quarks and gluons expected to appear from Quantum Chromodynamics during high energy collisions. Below, we examine the dynamical phase space of gluon transverse momenta near the so-called ``saturation'' phase including its fluctuation pattern. ``Saturation'' is expected to appear when the density of gluons emitted during the collision reaches the limit when recombination effects cannot be neglected, even in the perturbative QCD regime. We demonstrate that the gluon momenta exhibit a nontrivial clustering structure, analoguous to ``hot spots'', whose distributions are derived using an interesting matching with the thermodynamics of directed polymers on a tree with disorder and its ``spin-glass'' phase.

PACS numbers: 13.60.Hb, 12.38.Cy, 05.40.--a