Magnetic field lines have no end points. A set of field lines can form knots, links, braids, and tangles. As in knot theory, there are several invariants which can be employed to describe the topology of field lines. These include helicity integrals and average crossing numbers. Some relations of these integrals to magnetic energy will be described. In the description of both astrophysical and laboratory magnetic fields, one often deals with field lines with fixed end points on a boundary. The definitions of helicity need to be generalized to allow arbitrary boundary conditions. Periodic geometries such as the 3-torus are widely used in numerical simulations. The talk will discuss the fate of helicity integrals in such geometries.