Understanding how complex phenomena emerge from the collective action of agents driven out of equilibrium is fundamental to comprehending life processes at all scales. These phenomena also inspire designs for artificial materials, based on driven building blocks, that can replicate the remarkable adaptability and versatility of living matter. Unlike the familiar Hermitian operators that govern observables in closed passive systems, the dynamics of driven systems are described by non-Hermitian operators, which capture flows in energy and information generated by external or internal driving forces. As a result, their spectra can acquire complex eigenvalues, in stark contrast to the real energies or frequencies that characterize passive systems. In this talk, I’ll describe my group’s recent work in elucidating the physical consequences of imaginary components of energy and frequency in classical systems, ranging from coherent amplification of sound pulses in active mechanical metamaterials to delocalization transitions that mimic insulator breakdown in sheared polymer assemblies. These studies reveal new functionalities that can be achieved when active and driven agents with tunable interactions are used as the building blocks of designer materials.