Abstract: The fourth-generation light source — the X-ray free-electron laser (FEL) — has revolutionized the way science at the nano- to mesoscale is done. UCLA researchers have played a key role in this development, which is moving to a new phase: the birth of what is known as the fifth-generation light source — an ultracompact FEL or similar scheme that is driven by a beam derived from an advanced accelerator, a new class of accelerator based on lasers, plasmas, wakefields, and exotic structures. We discuss the characteristics of such a system, beginning with an overview of FEL gain mechanisms, noting that the future will bring beams with extreme high brightness and temporal scales down to the attosecond level. These attributes are synergistic with the characteristics of very high field — to the GV/m level — advanced accelerators, which must operate at quite small accelerating wavelength, demanding small charges and short pulses. In order to fully exploit such beams, a compact FEL system must also reimagine the undulator to utilize very short periods. This may be manifested in systems that vary from magnetostatic approaches using nanotechnology to plasma waves, as well as electromagnetic wave solutions that permit new types of narrow-spectrum light sources extending to gamma-ray emission. We highlight in this talk a few of the leading fifth-generation light source techniques, in both acceleration and radiation production, that are currently under active development at UCLA and its collaborators.