  We review the higher gauge symmetries in double and exceptional field theory
from the viewpoint of an embedding tensor construction. This is based on a
(typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of
representation $R$. The embedding tensor is a map from the representation space
$R$ into $\frak{g}$ satisfying a compatibility condition (`quadratic
constraint'). The Lie algebra structure on $\frak{g}$ is transported to a
Leibniz--Loday algebra on $R$, which in turn gives rise to an
$L_{\infty}$-structure. We review how the gauge structures of double and
exceptional field theory fit into this framework.
