Cepheid Variables
Measuring stars such as Polaris, Eta Aquilae and Delta Cephei allows astronomers to estimate the distances of faraway galaxies. Cepheid variables are supergiants with short periods, generally as short as one day to a few months long, during which they may brighten by as much as two magnitudes.
Mira Variables
Pulsating more irregularly than Cepheid variables are Mira variables, named for Mira in the constellation Cetus. The red giants pulsate over a longer period of time. For both types of stars, the mechanism of variation is fundamentally the same: A layer of ionized gas compressed by the inward force of gravity becomes more opaque as it compresses, lowering the brightness of the star and causing a buildup of heat. The heat increases the internal pressure of the star, causing it to expand until the gas layer is transparent again and greater amounts of light can escape, thus increasing the apparent brightness to an outside observer.
Binary Systems
Differing from the Cepheid and Mira "intrinsic" variable stars are binary stars with extrinsic variables. The stars themselves do not change, but their brightness as observed distantly does. In a binary system, two stars are locked in rotation around each another; as they eclipse each other, the brightness of the total system appears to change with a period equal to the time it takes for the stars to make a complete revolution.
Dying Stars
Growing colder and larger, as stars do as they age, causes a change in brightness and color as seen from Earth. This process is more of a one-way step. Perhaps the most dramatic variable star is the supernova, a star so massive that, when gravity finally overwhelms it, it contracts violently, producing a rebounding pulse of energy that tears the star apart, causing its brightness to increase tens of millions of times.