  We present several applications of the Assouad dimension, and the related
quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions
of orthogonal projections of sets. For example, we show that if the
(quasi-)Assouad dimension of $F \subseteq \rn$ is no greater than $m$, then the
box and packing dimensions of $F$ are preserved under orthogonal projections
onto almost all $m$-dimensional subspaces. We also show that the threshold $m$
for the (quasi-)Assouad dimension is sharp, and bound the dimension of the
exceptional set of projections strictly away from the dimension of the
Grassmannian.
