Gamma-ray burst (GRB) afterglows are riddled with multiscale processes in the spatial, temporal, and spectral domains. Accurately capturing the interplay between these processes, and their manifestations at short and long timescales, is the key to uncovering the nature and behavior of the associated progenitor and remnant. I will first focus on direct modeling and show how recent improvements in the treatment of the numerical dynamics, using moving meshes, allow us to correctly, numerically, simulate radiative cooling from non-thermal processes inside the jet. This finally allows for full broadband simulation of time-dependent synchrotron emission in relativistic transients. I will then present results showing how these simulations open the door to the study of complex dynamical behaviors with multiple emission sites (and the associated short-timescale light curve variability), as well as the investigation of the microphysical processes at play inside the jet in the trans-relativistic regime (and the associated late-time effects on the light curve). I will conclude by focusing on the inverse problem and present preliminary results on how state-of-the-art unsupervised machine leaning techniques can provide physical insight into the long-timescale behavior of GRB afterglows.