I will explain how to generate infinite families of rational balls from figure eight knot, which bound Rohlin invariant one Brieskorn homology spheres (a joint work with Kyle Larson). I will then discuss the question of when a contractible manifold fails to be a cork; this happens either if there is no exotic involution on its boundary, or it fails to be Stein. I will give examples of Stein non-corks, and non-Stein non-loose corks. I will discuss open questions of whether there are loose-corks that can not be corks, or if there are infinite order corks (this part is a joint work with Danny Ruberman).