Recent molecular photonics studies have highlighted the significant role that phase-structured light possessing orbital angular momentum (OAM) can have when interacting with matter. These studies discovered chiroptical effects sensitive to both the magnitude and sign of the optical OAM in both the absorption and scattering of twisted photons by molecules and nanoparticles. Specifically, it has been shown how a structured beam engaging with electric-quadrupole transitions in the material allows a unique sensitivity to the helical-phase structure of twisted light. In this paper we highlight experimental methodologies and systems suitable to observe and quantify the chiroptical processes of Rayleigh and Raman optical activity, and the newly discovered circular-vortex differential scattering effect with structured light—including the importance of off-axis beam alignment, input beam intensity structure, multipolar moments, and scattering-angle dependencies. It is shown that with a judicious choice of experimental setup, chiroptical effects that scale with the topological charge or OAM of the input beam enable optical activity signals to be enhanced and significantly exceed those based solely on circularly polarized, unstructured light. The new technique thus offers a highly useful and important spectroscopic application of structured light. The more detailed role that perfect optical vortices with high OAM will play in such optical activity effects is now highlighted, to show where there is substantial scope for experimental application, specifically in vibrational optical activity and chiral spectroscopy.