Phosphorescent polymer light-emitting diodes (PhPLEDs) are promising devices in flat panel displays and solid state lighting sources since they can combine the advantages of the high efficiency of electrophosphorescence and low-cost, large-scale manufacture by using a solution process. However, their efficiencies are generally much lower than those of small-molecule-based devices fabricated by using a thermal deposition approach. One of the major reasons for their low efficiency is that energy is lost by back transfer to a polymer host. This tutorial review gives a brief introduction to the fundamentals of PhPLEDs, and then highlights recent progress in the main approaches to suppress triplet energy back transfer from the phosphor to the polymer host towards realizing highly efficient PhPLEDs. The suppressing mechanisms are discussed, and the achievement of high device efficiencies are demonstrated. Emphasis is placed on the relationships between molecular structure, the extent of suppressing triplet energy back transfer, and device performance.