Polyhedral compilation has evolved for nearly three decades, being implemented as a building block or an optional extension of numerous open-source and/or commercial compilers. On the one hand, the polyhedral model is equipped with wider range of applications, more powerful expressiveness and greater optimization space when compared with those traditional models adopted for parallelizing compilers, thus representing the state of the art of almost each domain of parallelizing compilers and becoming a hot topic to a great number of international research teams working on compilers. On the other hand, the polyhedral model is also characterized as being difficult in theory, complex for manipulation, and diverse with challenges, hampering its adoption in underdeveloped countries and areas and drawing few researchers working on this topic from the domestic compiler community. Aiming at opening the "black-box" of the polyhedral model, this paper conducts a survey on the "black magic" of polyhedral compilation. First, the underlaying theory behind the polyhedral model is introduced along with a desciption of the general compilation process and an overview of the research directions. Next, the research progress of the polyhedral compilation targeting on parallelism, data locality, and extensions in various application domains is presented. Last but not least, open challenges faced by the polyhedral community and potential research directions on this topic are disussed. The purpose of this work is to provide an important reference for the domestic compiler community by reviewing and summarizing current trends on the polyhedral compilation, and to promote Chinese compiler researchers in making progress on this topic.