abstract: In this talk I will discuss digit frequencies in the setting of expansions in non-integer bases, and self-affine sets with non-empty interior. Within expansions in non-integer bases we give conditions guaranteeing every x has an expansion which is simply normal, and an expansion for which the digit frequency does not exist. The same techniques can also be used to study a class of planar self-affine sets. We show that if the horizontal contraction lies in a certain parameter space and the vertical contractions are sufficiently close to 1, then every nontrivial vertical fibre contains an interval. Our approach lends itself to explicit calculation and give rise to new examples of self-affine sets with non-empty interior.