The Pulsating (called also oscillating) Heat Pipe (PHP) is a high performance passive heat transfer device. It consists in a closed capillary channel folded into several meanders, evacuated, and partially filled with a liquid and its vapor. One side is in thermal contact with a hot spot, the other with a cold spot. The oscillation of the liquid plugs and vapor bubbles spontaneously occurs after the heating beginning. The heat exchange takes place not only by latent heat transfer, but also by liquid convection. Both this advantage and the PHP structural simplicity make it competitive with respect to other kinds of heat pipes. However, the PHP operation is non-stationary and depends on many physical and material parameters. As a result, application of empirical correlations is quite unsuccessful. More sophisticated direct modeling is thus required. In this review, we present the past, present, and future perspectives of the theoretical PHP studies. The physical phenomena on the level of a single bubble and single liquid plug is addressed first. In this context, the modeling of the simplest, single branch PHP is described as a necessary first step toward the PHP understanding and model validation. The modeling of interaction between the bubbles and plugs (bubble generation and disappearance, plug evaporation) is discussed next. Finally, the state of the art of the physical modeling and simulation of the multi-turn PHP is reviewed and the difference between existing approaches is explained.