As the complex version of Ricci flow, K\"ahler-Ricci flow enjoys the special feature, i.e., cohomology information for the evolving K\"ahler metric. The flow can thus be reduced to scalar level as first used by H. D. Cao in the alternative proof of Calabi's Conjecture. People have mostly been focusing on the situation when the K\"ahler class is fixed. As first considered by H. Tsuji, by allowing the class to evolve, the flow can be applied in the study of degenerate class, for example, class on the boundary of K\"ahler cone. We discuss some results in this drection. This is the geometric analysis aspect of Tian's program, which aims at applying K\"ahler-Ricci flow in the study of algebraic geometry objects with great interests.