In this non-technical talk we will discuss the role of Lusternik-Schnirelmann theory in multiplicity results for closed Reeb orbits. In particular, we will show how a variant of this theory is used in the proofs of new multiplicity results for simple closed Reeb orbits on the standard contact sphere, the unit cotangent bundle to the sphere and some other contact manifolds. The talk is based on a joint work with Basak Gurel.