  It was noticed many years ago, in the framework of massless RG flows, that
the irrelevant composite operator $T \bar{T}$, built with the components of the
energy-momentum tensor, enjoys very special properties in 2D quantum field
theories, and can be regarded as a peculiar kind of integrable perturbation.
Novel interesting features of this operator have recently emerged from the
study of effective string theory models.In this paper we study further
properties of this distinguished perturbation. We discuss how it affects the
energy levels and one-point functions of a general 2D QFT in finite volume
through a surprising relation with a simple hydrodynamic equation. In the case
of the perturbation of CFTs, adapting a result by L\"uscher and Weisz we give a
compact expression for the partition function on a finite-length cylinder and
make a connection with the exact $g$-function method. We argue that, at the
classical level, the deformation naturally maps the action of $N$ massless free
bosons into the Nambu-Goto action in static gauge, in $N+2$ target space
dimensions, and we briefly discuss a possible interpretation of this result in
the context of effective string models.
