The formation of gas-giant planets needs to happen before the primordial gas-rich disk dissipates in ~ 6 Myr, while the formation of terrestrial planets and massive planets beyond the ice line is not limited by the presence of gas in the disk and can continue for approximately 100 Myr; a critical step in this latter process is the formation of planetesimals. Observations with the Spitzer Space Telescope showed that there is evidence that at least 15% of mature stars (10 Myr-10 Gyr) of a wide range of masses (0.5-3 MSun) harbor planetesimal belts with sizes of 10s-100s AU. This evidence comes from the presence of an infrared emission in excess of that expected from the stellar photosphere, thought to arise from a circumstellar dust disk. The reason why these dust disks are evidence of the presence of planetesimals is because the lifetime of the dust grains (< 1 Myr) is much shorter than the age of the star (> 10 Myr); therefore, the origin of these dust grains cannot be primordial but must be the result of on-going dust production generated by the collision, disruption or sublimation of planetesimals like the asteroids, comets and Kuiper Belt objects (KBOs) in our solar system. The discovery of the debris disk phenomenon in 1986, a decade before the identification of extra-solar planets around main sequence stars, provided the first evidence that a critical step in the process of planet formation (the formation of planetesimals) is taking place around other stars. The presence of debris disks (and therefore planetesimals) around stars with a very wide range of spectral types, from M-type to the progenitors of white dwarfs - with several orders of magnitude difference in stellar luminosities - implies that planetesimal formation is a robust process that can take place under a wide range of conditions. The study of debris disks sheds light on the formation, evolution and diversity of planetary systems.