Pushing the boundaries with T$\overline{T}$

In this talk, I will provide a pedagogical introduction to $T\overline{T}$ deformations of conformal field theories (CFTs)- broadly speaking, these constitute a class of interesting, yet solvable, irrelevant perturbations of arbitrary (two-dimensional) CFTs. After motivating why one should be interested in such constructions, I will outline relevant field-theoretic developments on such irrelevant deformations. This done, I will survey the current perspective on the (Anti-de Sitter) holographic interpretation of such CFTs. Time permitting, I will conclude with a brief review of recent (possibly speculative) developments suggesting that $T\overline{T}$ CFTs could provide a pathway to holographic descriptions beyond AdS holography.