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