We shall present some general techniques for studying projective embedded manifolds uniruled by lines, based on the Hilbert scheme of lines passing through a general point of the manifold and contained in it. The main applications will be the proofs of Hartshorne Conjecture for quadratic manifolds, of the classification of quadratic Hartshorne varieties, of the classification of Severi varieties. Our approach will show many connections between these problems, which were overlooked before, and also a uniform way of solving them. If time allows, we shall also discuss some open problems including the Barth-Ionescu Conjecture.