We first review some basic facts of contact and symplectic topology. Symplectic cobordisms are the objects that bring these two worlds together: they are symplectic manifolds with contact manifolds as their boundary. Lagrangian submanifolds in a symplectic cobordism limit to Legendrian submanifolds on the boundary. When the symplectic manifold is four-dimensional and the contact manifolds are three-dimensional, the Legendrian submanifolds are knots and links. We review certain restrictions on the classical invariants of such Legendrian knots imposed by the relation of Lagrangian cobordism. Then we specialize to Legendrian knots in the 3-sphere as the boundary of Lagrangian surfaces in the 4-ball. Much of the recent research in this area uses tools related to contact homology. In particular, we explore the notion of a ruling of a Legendrian knot. After defining the ruling polynomial, we show several new ways to compute it, including the extension of a skein relation for ungraded rulings to integer graded rulings. We show how certain kinds of ribbon knots always give rise to rulings. Finally, we construct for any ruled Legendrian knot an immersed Lagrangian surface bounded by the knot.