Summary: We ponder a different kind of complex synchronization. We name this sort “complex phase synchronization” (CPHS). This review concentrates on two chaotic complex structures, including a similar structure of direct terms with totally differing or incompletely in nonlinear terms. A novel plan is needed to complete the complex phase synchronization (CPHS) for the chaotic complex structures. In this plan, we have utilized the dependability hypothesis to decide diagnostically the complex control capacities that are expected to accomplish CPHS. From this plan, we found that CPHS holds or incorporates two sorts of synchronizations (phase and anti-phase synchronizations) and the state factors of the main structure synchronize with alternate state factors of the slave structure. We connected this plan, for instance, to study the CPHS of two chaotic complex Lü structures with incompletely changing in nonlinear terms. These complex (or mind-boggling) structures resemble in various imperative areas of mineral science and building. Numerical outcomes are sketched out to uncover the phases and modules errors of these chaotic attractors, subsequently communicating that CPHS is fulfilled. A specific application in secure communication is designed. Amongst this secure communication, CPHS between transmitter and collector is the key to the information signs are regained.