MUSE has revolutionized the spectroscopy of dense stellar populations. Its wavelength-dependent spatial information, combined with the instrument's performance, allows for the simultaneous acquisition of spectra from thousands of individual stars, even in the dense cores of galactic globular clusters (GCs). This capability enables detailed investigations of stellar properties in which the wavelength resolution of MUSE facilitates the study of GC dynamics through radial velocity (RV) measurements. The RV sensitivity is sufficient to detect a variety of binaries in GCs, including exotic types. Given that the orbital kinetic energy of binaries is fundamental to the evolution of GCs as an energy source, it is crucial to investigate the binary properties of GCs, a task made feasible with MUSE. This allows for the comparison of predicted binary properties from numerical simulations of GCs with observed ones, thereby calibrating binary evolution modeling in dense stellar environments. Such calibration is essential for better disentangling the kinematic signatures of potential intermediate-mass black holes from, for example, sub-clusters of binaries with massive compact companions (black holes, neutron stars, or white dwarfs). In this talk, we will report on our long-term monitoring of GCs using MUSE, summarize the results concerning binary properties, and compare these findings to model predictions. We will also briefly discuss the prospects for upcoming ESO instruments.