Recent advancements in polarization and wavefront control, as well as the brilliance and duration of X-ray pulses at FELs and synchrotrons, have been achieved. These upgraded photon source characteristics open up new opportunities to obtain both spatial and spectroscopic information on molecular structures and dynamics.
First, a perturbative formalism that enables the description of a wide range of nonlinear optical and X-ray signals will be reviewed. Next, experiments and theoretical proposals using these advancements in nonlinear and chirally-sensitive spectroscopies will be discussed. Finally, spectroscopies using twisted beams carrying orbital angular momentum will be presented.