Morse theory is a powerful tool for analyzing the topology of a manifold by studying the critical points of a smooth function. The theory constructs Morse homology from the space of gradient flow trajectories, which provides a topological invariant that is isomorphic to singular homology. In this talk, we will apply Morse theory to the area functional, focusing on low area min-max critical points and the existence of trajectories connecting them. This talk is based on joint work with P. Gaspar.