Motivated by the growing demand to integrate functional oxides with dissimilar materials, numerous studies have been undertaken to detach a functional oxide film from its original substrate, effectively forming a membrane, which can then be affixed to the desired host material. This review article is centered on the synthesis of functional oxide membranes, encompassing various approaches to their synthesis, exfoliation, and transfer techniques. First, we explore the characteristics of thin-film growth techniques with emphasis on molecular beam epitaxy. We then examine the fundamental principles and pivotal factors underlying three key approaches of creating membranes: (i) chemical lift-off, (ii) the two-dimensional layer-assisted lift-off, and (iii) spalling. We review the methods of exfoliation and transfer for each approach. Last, we provide an outlook into the future of oxide membranes, highlighting their applications and emerging properties.