  In this paper, we study the quasisymmetric embeddability of weak tangents of
metric spaces. We first show that quasisymmetric embeddability is hereditary,
i.e., if $X$ can be quasisymmetrically embedded into $Y$, then every weak
tangent of $X$ can be quasisymmetrically embedded into some weak tangent of
$Y$, given that $X$ is proper and doubling. However, the converse is not true
in general; we will illustrate this with several counterexamples. In special
situations, we are able to show that the embeddability of weak tangents implies
global or local embeddability of the ambient space. Finally, we apply our
results to Gromov hyperbolic groups and visual spheres of expanding Thurston
maps.
