Saturation of the light-matter interaction is a general non-linear feature of material systems, be they atoms or semiconductors. A saturable absorber exhibits an absorption coefficient that depends on the incident intensity. In semiconductors, the possibility of judiciously controlling saturation phenomena is of great importance for fundamental physics as well as applications. A seminal example is the development of the semiconductor saturable absorber mirror (SESAM) based on interband transitions in quantum wells, that revolutionized the field of ultra-fast lasers in the vis/near-IR spectral range, allowing ultra-fast lasers pulses. Ultra-fast lasers based on SESAMs find applications in several domains, and even in quantum phenomena.