A knot K is fibered if its complement in the 3-sphere admits a fiber bundle structure over S^1 that is well-behaved near K. In the topology class last semester, there was a **knotty** homework question that asked one to prove the trefoil is fibered with the fibers being punctured tori. The question of whether or not a knot is fibered and, more generally, whether or not a manifold is a fiber bundle over S^1 are surprisingly related to circle-valued Morse theory and Novikov homology, which generalize the classical Morse theory and Morse homology. In this talk, I will introduce Morse theory and circle-valued Morse theory, and explore their applications to detecting fibrations of manifolds over the circle.