Freestanding oxide membranes have recently emerged as a promising platform, offering new opportunities for experimentalists to design materials with novel properties. These membranes, typically consisting of transition metal oxides, can be synthesized as freestanding ultra-thin quasi-2D layers and, subsequently, reassembled into multilayer stacks with controlled relative twist angles. In these heterostructures, controlling the moiré superlattices pattern of the two lattices can play a crucial role in creating unique and new electronic, optical, magnetic, and mechanical properties that do not exist in the individual constituent materials or in traditional non-twisted epitaxial heterostructures. Here, we explore the role of stacking and twisting of freestanding oxide membranes, including the underlying principles and potential applications. We also discuss the current challenges and provide a perspective on some of the possible future directions of the field. Our aim is to highlight the opportunities for creating new functional materials by stacking and twisting freestanding oxide membranes.