The Gelfand-Graev or Whittaker space for p-adic groups plays a central role in different branches of representation theory. After explaining some basics of this object, I will consider two variants: the first is for p-adic loop groups and the second is for metaplectic covers of reductive groups. Studying the first case leads us to a novel definition of deformed weight multiply for affine Lie algebras; studying the second leads us to connection with quantum groups at roots of unity.