Understanding disordered systems--materials with constituent particles that lack long-range order--has been a persistent challenge in condensed matter physics. These systems are ubiquitous in nature, and display themselves on a wide variety of length scales from Angstroms (atomic and molecular glasses, polymers) to micrometers (colloidal suspensions, powders) and even meters (mudslides and boulders). A central question in this field has been ``what is the relationship between constituent-level structure and dynamics in these systems, and how does it lead to bulk behavior (viscosity, strength, or plasticity)?'' In recent years, two directions of attack have proven effective in uncovering this complex relationship: analysis of the low-frequency quasilocalized excitations of these systems, and the application of data-driven machine-learning methods. In this thesis, we focus on three main topics. First, we explore the connections between machine-learned softness and thermodynamic excess entropy in supercooled liquids, leading to the collapse of energy barriers as a function of the excess entropy. After this, we analyze annealed 2D glasses under oscillatory shear with small thermal activation well below $T_g$. Our results show an unexpected diffusive behavior just below AQS yielding that is dependent upon the preparation history. These results are followed by an analysis of the correlation of the soft modes and softness with the reversible plastic rearrangements under oscillatory shear. Finally, we end with preliminary results on the statistics of soft quasilocalized excitations before and after training under oscillatory shear.