The formation and composition of planets and their atmospheres are among the most intriguing and challenging scientific topics. The outcome of planet formation and the resulting planetary systems' architectures are set by the initial conditions in the birth sites of planetary systems – planet-forming disks. These planet-forming disks are a natural outcome of the star formation process. The solar nebula, out of which the solar system emerged about 4.5 Gy ago, is one example of such an environment. In addition, hundreds of planet-forming systems are routinely observed nowadays in the dust continuum and multiple atomic and molecular lines (from optics to radio wavelengths). In my KoCo talk, I will show how the observations and theoretical models are used to infer key disk properties and present our current understanding of disk thermal and density structures, masses, dynamics, grain properties, and chemical composition. I will talk about how various processes during star and planet formation affect the resulting spatial distributions and abundances of various ices and gaseous species, ranging from simple inorganic to complex organic molecules. Last but not least, I will also briefly talk about how the physical and chemical properties of these disks are linked to the physical properties and chemical composition of the emerging terrestrial rocky and gas giant planets, as well as primitive bodies such as asteroids and comets.