Corner-shared coordination polyhedral crystals (CSCPCs) represented by perovskites have unique and various properties in optics, electrics, and magnetism, leading to their broad applications such as in serving as ferroelectric material, fast ionic conductors, and electro/photo-catalysts. However, the excellent properties are owned only by a very small fraction of CSCPS phases. How to obtain such phases through structural operation has always been a research hotspot and a bottleneck in related fields. Herein, we review the recent research progress of the synthesis of high-performance CSCPC materials from the perspective of phase structure, in order to clarify the intrinsic rules of phase evolution and reveal the mechanism behind the phase manipulation. We first systematically summarize the types of polyhedra and crystal frameworks in CSCPCs and classify the polyhedral distortions as three main types, i.e. cation displacements, polyhedral rotations, and deformations. Based on that, we further analyze and conclude different material synthesis methods. We find that most traditional synthesis methods rely on the phase transitions induced by the change of external physical conditions at a macroscopic level, such as composition, temperature, and pressure. Recently, there was an emerging synthesis method focusing on the microscopic manipulation of polyhedral geometry and topology, such as phase constructions according to tolerance-factor and substrate-proximity effects. The macroscopic synthesis methods and the microscopic synthesis methods share the same phase manipulation mechanism: making crystals transit into the structure-specified phases by inducing polyhedral distortions. The only difference is that the latter is more target-oriented, but its applications are currently limited to octahedral coordination tilt/rotation systems. Expanding its application scope is still a challenge. In addition, we propose two aspects that may be useful in optimizing the synthesis method: one is to clarify the origin of induced distortions and the interaction between different distortions, and the other is to customize the guidelines based on computer science. We hope that the research progress reviewed in this article can provide some valuable references and inspirations for designing and synthesizing the high-performance CSCPC materials.