  We revisit curious objects in string and M-theory called exotic
brane---objects that are highly non-perturbative, possessing a tension that
scales less than $g_s^{-2}$ and are generically of low-codimension. They are
non-geometric in the sense that they are only well-defined locally as
supergravity solutions and require duality transformations to patch correctly,
in addition to the usual diffeomorphisms and gauge transformations.
  We argue that Double Field Theory (DFT) and Exceptional Field Theory (EFT)
are the prime setting in which to examine such objects. To emphasise this, we
construct an explicit solution in $E_{7(7)} \times \mathbb{R}^+$ EFT that
unifies many of the codimension-2 exotic branes into a single well-behaved
solution on an extended spacetime. We further argue that there are in fact an
infinite number of exotic branes in string- and M-theory, many of which fall
into a more general class of exotic branes that do not afford even a local
description in terms of conventional supergravity.
