We discuss a recent theory for studying many-body effects in nonlinear spectroscopy. With a canonical transformation, we eliminate the optically-induced interband charge fluctuations and obtain a "dressed" Hamiltonian describing the Coulomb correlations leading to excitonic resonances. We then focus on a Fermi sea and use the Coupled Cluster expansion to study the dephasing and many-body processes. We provide an intuitive picture of how the dynamics of the Coulomb correlations manifests itself in nonlinear spectroscopy within the conventional picture of interacting carriers moving inside effective bands. We then apply this general method to extract the physics conveyed by recent experiments, indicating that, for off-resonant pump excitation, the different nature of the excitonic effects in doped quantum wells or metals (Fermi Edge Singularity) and undoped semiconductors (atomic exciton) leads to different nonlinear absorption. To interpret this, we demonstrate how a pump-induced increase in the carrier masses strongly enhances the Fermi Edge Singularity and why this depends on the pulse duration.