The recently introduced concept of growth envelopes characterises the unboundedness of functions in spaces of Sobolev or Besov type by its non-increasing rearrangement. Similarly one can focus on questions of (Lipschitz) continuity using the (classical) modulus of continuity, this leads to continuity envelopes. We explain basic ideas, present some recent results -- including also spaces defined on fractal h-sets -- and give applications in the context of limiting embeddings or asymptotic estimates for approximation numbers.