Abstract: One of the most fascinating aspects of intense (> 10¹⁹ W/cm²) laser-plasma interactions is the generation of high-current relativistic electron beams. The propagation of these relativistic electron beams is exciting as it enables the heating of dense plasmas, the production of sources of high-performance x-rays and ions for other applications, and the possibility of “igniting” fusion experiments via the fast ignition concept. This talk will focus on the processes that enable these beams to propagate through solid materials and how detailed x-ray spectroscopy provides insights into the fundamental physics at play. The discussion will outline how x-ray spectroscopy can provide information associated with the electron beam current, divergence and energy distributions. The basics of laser-target interactions and diagnostic technologies needed to extract robust information, as well as the interpretation of spectroscopic measurements via plasma-kinetic and detailed collisional–radiative atomic physics simulations are described.