Are there exotic copies of S^4 or CP^2 ?. It is known that if they exist they must contain 1- or 3- handles. About 24 years ago Donaldson gave the first example of an exotic smooth 4-manifold, i.e. he proved that Dolgachev's complex surface E(1)_{2,3} is an exotic copy of CP^2 # 9(- CP^2); right about the same time Harer Kas and Kirby wrote a book about E(1)_{2,3} where they conjectured that it must contain 1- or 3- handles. We will discuss the recent solution of this conjecture (in the negative). In this context we will relate the proof to "corks" and "plugs", which are roughly freely floating objects in 4- manifolds determining their exotic structures