We discuss the development of a new generation of accelerator-based hard X-ray sources driven exclusively by laser light. High-intensity laser pulses serve the dual roles: first, accelerating electrons by laser-driven plasma wakefields, and second, generating X-rays by inverse Compton scattering. Such all-laser-driven X-rays have recently been demonstrated to be energetic, tunable, relatively narrow in bandwidth, short pulsed and well collimated. Such characteristics, especially from a compact source, are highly advantageous for numerous advanced X-ray applications-in metrology, biomedicine, materials, ultrafast phenomena, radiology and fundamental physics.