Given a locally compact group G, the full C*-algebra C*(G) and reduced C*-algebra C*_r(G) are well known. But already Eymard in his fundamental paper in 1964 realized that there are a lot of algebras in between. Until recently these “exotic” C*-algebras in between has received little attention. I will try to give a survey of these algebras and explain how they give rise to exotic crossed products and exotic coactions. However, we have more questions than answers. This is joint work with Steve Kaliszewski and John Quigg.