A class of isotope effects that alters isotope ratios on a mass-independent basis provides a tool for studying a wide range of processes in atmospheres of Earth and other planets as well as early processes in the solar nebula. The mechanism for the effect remains uncertain. Mass-independent isotopic compositions have been observed in O$_3$, CO$_2$, N$_2$O, and CO in Earth's atmosphere and in carbonate from a martian meteorite, which suggests a role for mass-independent processes in the atmosphere of Mars. Observed mass-independent meteoritic oxygen and sulfur isotopic compositions may derive from chemical processes in the presolar nebula, and their distributions could provide insight into early solar system evolution.