It is believed that gravity is holographic, namely that the gravitational dynamics in a given spacetime (region) can be encoded by a non-gravitational theory living on the boundary of that region. The AdS/CFT correspondence is an extremely successful concrete realization of the holographic idea; however, generalizing the holographic dictionary beyond AdS/CFT has proven to be difficult. My work focuses on the - rather general - instances of non-AdS holography  where the boundary theory can be argued to correspond to a finely-tuned finite irrelevant deformation of a conformal field theory (CFT). In this context, I will discuss the properties of two exactly solvable irrelevant deformations of two-dimensional CFTs known as $T\bar T$ and $J\bar T$ - deformed CFTs and the lessons they teach us about non-AdS holography.