The MUSE revolution: The enormous impact of MUSE on strong gravitational lensing by galaxy clusters.

The advent of MUSE has marked an unprecedented revolution in the field of strong gravitational lensing (SL) by galaxy clusters (GCs), allowing us to complement the exquisite photometric data obtained by the Hubble Space Telescope (e.g., CLASH and HFF campaigns) with a third crucial spectroscopic dimension. I will present the details of this MUSE revolution that has elevated the SL by GCs to be the most powerful technique to investigate some of the greatest mysteries of modern astrophysics. MUSE is essential in both identifying a large number of secure multiple images and pure and complete samples of cluster galaxies. Additionally, it enables the measurement of the stellar velocity dispersion of a significant fraction of GC members, which is crucial for calibrating their total mass within SL models. I will discuss the significant impact of MUSE data on our SL model of the GC MACS0416 (z=0.396). This benefited from the deepest MUSE pointing ever observed on a lens GC field, enabling the identification of one the largest sample (237) of secure multiple images ever used in SL to date. The synergy between MUSE and photometric data has reached its maximum expression with the JWST. In this context, I will present a high-precision SL model for the GC Abell 2744 (z=0.307), which includes 149 multiple images. Finally, I will demonstrate how, thanks to an innovative SL code (Gravity.jl), we can combine SL and MUSE data for the study of the dynamics of lensed galaxies at high redshifts.