Complex-oxide materials are gaining a tremendous amount of interest in the semiconductor materials and device community as they hold many useful intrinsic physical properties such as ferro/piezoelectricity, pyroelectricity, ferromagnetism, as well as magnetostriction and other properties suitable for energy storage elements. Complex-oxides can also be complemented with conventional semiconductor-based devices or used by themselves to realize state-of-the-art electronic/photonic/quantum information devices. However, because complex-oxide materials have vastly different crystalline structures and lattice constant difference compared to conventional semiconductor devices (such as Si or III-V/III-N materials), integration of complex-oxides onto conventional semiconductor platforms has been difficult. Thus, there has been constant efforts to produce freestanding single-crystalline complex-oxide thin films such that these films can be transferred and integrated together with device platforms based on other materials. This review will provide a comprehensive review on single-crystalline complex-oxide membranes technology developed thus far: how they are synthesized, methods to release them from the substrate, and their outstanding properties and applications.