Complex oxide heterostructures provide material platforms to create novel states not found in the bulk constituents. Another approach to the low-dimensional oxide physics is to generate freestanding two-dimensional (2D) oxide membranes that offer a significant degree of freedom to control physical properties. The talk will be focused on two research directions to challenge the limit of complex oxide materials. The first topic is the ultrathin limit of oxide membranes, where the membrane faces an intrinsic 2D limit of the crystalline order described by the Berezinskii – Kosterlitz – Thouless transition. The second part is about extreme strain engineering and phase control in oxide membranes. In the example of magnetic oxide membranes, we demonstrate full control of the electromagnetic ground states via the systematic strain design, constructing a new phase diagram inaccessible by bulk and thin film techniques.