How can we understand all coherent sheaves on a projective scheme? Quot schemes offer a geometric answer by parameterizing the sheaves, and the Hilbert polynomial gives a natural stratificaiton into disjoint pieces. We will survey the key features of these parameter spaces for the quotients of a finite direct sum of the structure sheaf on projective space. Moreover, we will complete classify the smooth Quot schemes of this form. This talk is based on joint work with Roy Skjelnes and Mike Stillman.