  We show that method of characteristics provides a powerful new point of view
on $T\bar{T}$-and related deformations. Previously, the method of
characteristics has been applied to $T\bar{T}$-deformation mainly to solve
Burgers' equation, which governs the deformation of the \emph{quantum}
spectrum. In the current work, we study \emph{classical} deformed quantities
using this method and show that $T\bar{T}$ flow can be seen as a characteristic
flow. Exploiting this point of view, we re-derive a number of important known
results and obtain interesting new ones. We prove the equivalence between
dynamical change of coordinates and the generalized light-cone gauge approaches
to $T\bar{T}$-deformation. We find the deformed Lagrangians for a class of
$T\bar{T}$-like deformations in higher dimensions and the
$(T\bar{T})^{\alpha}$-deformation in 2d with generic $\alpha$, generalizing
recent results in arXiv:2206.03415 and arXiv:2206.10515.
