Owing to the rapid development of microelectronic technology,higher requirements are raised for miniaturization, intellectualization,sensitivity,reliability,low-power consumption and versatile functions of electromagnetic functional devices,but conventional block magnetic or electrical functional materials cannot meet those requirements mentioned above any longer.Layered magnetoelectric composites,by contrast,have ferroelectric,ferromagnetic and magnetoelectric properties,so they are possible to satisfy these demands above and be applied to the next-generation magnetoelectric functional devices.Layered magnetoelectric composites not only have rich physical phenomena and effects,but also possess broad application prospects in weak magnetic field detectors,multi-state memories,electric-write/magnetic-read memories,electrically tunable filters,phase shifters,antennas,etc,which have attracted extensive attention of material scientists and physicists.Among layered magnetoelectric composites,the functional thin film/ferroelectric single crystal heterostructures have aroused increasingly interest due to their simple preparation method,flexible structural design,effective electric field control and low power consumption.Currently,because of the excellent ferroelectric and piezoelectric properties of the (1 -x) PbMg1/3Nb2/3O3-xPbTiO3(PMN-PT) single crystal,the functional thin film/PMN-PT single crystal heterostructure has become one of the hot research topics in the multiferroic composite thin film material field.On this research topic,Chinese scientists have made their own significant contributions to the research of functional thin film/PMN-PT single crystal heterojunction.So far,researchers have built multiple types of thin film/PMN-PT heterostructures,such as manganese oxide/PMN-PT,ferrite/PMN-PT,ferromagnetic metal/PMN-PT,dilute magnetic semiconductor/PMN-PT,luminescent material/PMN-PT,two-dimensional material/PMN-PT,multi-layer film/PMN-PT,superconductive material/PMN-PT,etc.,and they have made great achievements in both theoretical and experimental studies.In this review,we summarize the research progress of magnetoelectric composite thin films based on PMN-PT single crystal substrates in the last decade.We first briefly describe the current status of articles related to functional film/PMN-PT heterostructures.Then we introduce the phase diagram and electric-field-induced strain properties of the PMN-PT single crystal around the morphotropic phase boundary.We also classify the heterostructures according to different categories of functional thin film materials and discuss the representative research findings of each category in the past few years.Our discussion focuses on the magnetoelectric properties of materials and the intrinsic physical mechanism.Finally,we also discuss the scientific problems to be solved and predict the possible application directions in the future.