In the interaction between an intensely powerful laser pulse and a solid target, a phenomenon occurs where the laser causes the surface plasma density of the target to modulate, creating what is known as a relativistic oscillating mirror. This mirror produces sequences of attosecond pulses, which are essentially phase-locked harmonics, that move at the angle of reflection due to the high-speed oscillation of the electrons on the surface. Our recent findings demonstrate that in specific scenarios, the surface of the mirror experiences self-modulation, resulting in the nanoscale bunching of electrons and the subsequent emission of intense, coherent extreme ultraviolet (XUV) light that travels along the surface, defying the conventional law of reflection. This process is identified as being more efficient in generating XUV light than the existing methods that utilize laser-driven sources, highlighting its significant potential for both scientific and technological applications. Furthermore, we present results from our ongoing research on the generation of coherent light from relativistic plasma mirrors moving at a uniform speed, which are established by the non-linear plasma waves initiated by either laser pulses or relativistic beams of charged particles.