TTbar-deformed theories provide a unique perspective on both QFT, beyond the Wilsonian paradigm, and on holography, beyond the standard asymptotic boundary conditions. To understand how these theories are organized, I will discuss their locality structure through the infinite-dimensional field-dependent symmetries, which they inherit from the conformal group. Analyzing the symmetry generators both semi-classically and as quantum operators, we find that these theories are quasi-local and contain free parameters, revealing potential ambiguities in the Hamiltonian formulation. I will discuss some of the implications for the holographic interpretation and illustrate with an example where everything can be calculated explicitly at the semi-classical level, thus providing a litmus test for different proposals in the literature.