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R4 is one of the most mysterious Euclidean spaces. It admits a continuum of smooth structures, yet if n is not 4, Rn has only one smooth structure. Another peculiarity is that R4 is the only Euclidean space for which we do not know the answer to the smooth Schoenflies problem. One rather naive approach to study the geometry of R4 is to ask which 3-manifolds appear as smooth submanifolds of R4. Hantsche and Whitney were the first to make progress on this problem, roughly 70 years ago. Only a handful of people have made progress on this problem since. I will try to bring you up to date on what is known about this problem, going into details on some of the more easily understood constructions.