Brilliant light sources, such as free-electron lasers, are an essential tool for a multidisciplinary research community, ranging from medicine and life sciences to fundamental physics, as they enable new insights into processes on atomic length and time scales. Laser-plasma accelerators bear the promise to drive future compact free-electron lasers. A high-energy laser pulse excites a density perturbation in a plasma, generating large electric fields, which can accelerate electron beams to GeV scale energies over only a few centimeters acceleration length. Synchronized to an optical laser and with intrinsic pulse lengths on a few-femtosecond scale, an X-ray beam derived from such a bunch promises highest temporal resolution. Here, an introduction to the basic physics of laser-plasma acceleration and its recent development will be given, followed by a brief discourse on the theory of free-electron lasers. Based on this, we discuss the challenges arising when designing a laser-plasma-based free-electron laser.