The interstellar medium (ISM) is subject, on one hand, to heating and cooling processes that tend to segregate it into distinct phases due to thermal instability (TI), and on the other, to turbulence-driving mechanisms that tend to produce strong nonlinear fluctuations in all the thermodynamic variables. In this regime, large-scale turbulent compressions in the stable warm neutral medium (WNM) dominate the clump-formation process rather than the linear developent of TI. Cold clumps formed by this mechanism are still often bounded by sharp density and temperature discontinuities, which however are not contact discontinuities as in the classical 2-phase model, but rather “phase transition fronts”, across which there is net mass and momentum flux from the WNM into the clumps. The clumps grow mainly by accretion through their boundaries, are in both thermal and ram pressure balance with their surroundings, and are internally turbulent as well, thus also having significant density fluctuations inside. The temperature and density of the cold and warm gas around the phase transition fronts fluctuate with time and location due to fluctuations in the turbulent pressure. Moreover, shock-compressed diffuse unstable gas can remain in the unstable regime for up to a few Myr before it undergoes a phase transition to the cold phase, and is furthermore constantly replenished by the turbulence. These processes populate the classically forbidden density and temperature ranges. Since gas at all temperatures appears to be present in bi- or tri-stable turbulence, we conclude that the word “phase” applies only locally, surrounding phase transition sites in the gas. Globally, the word “phase” must relax its meaning to simply denote a certain temperature or density range.