In physics (especially astrophysics), redshift happens when light seen coming from an object that is moving away is proportionally increased in wavelength, or shifted to the red end of the spectrum. More generally, where an observer detects electromagnetic radiation outside the visible spectrum, "redder" amounts to a technical shorthand for "increase in electromagnetic wavelength" — which also implies lower frequency and photon energy in accord with, respectively, the wave and quantum theories of light.
Redshifts are attributable to the Doppler effect, familiar in the changes in the apparent pitches of sirens and frequency of the sound waves emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer. Cosmological redshift is seen due to the expansion of the universe, and sufficiently distant light sources (generally more than a few million light years away) show redshift corresponding to the rate of increase of their distance from Earth. Finally, gravitational redshifts are a relativistic effect observed in electromagnetic radiation moving out of gravitational fields. Conversely, a decrease in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field.
Although observing redshifts and blueshifts have several terrestrial applications (e.g., Doppler radar and radar guns), redshifts are most famously seen in the spectroscopic observations of astronomical objects.
A special relativistic redshift formula (and its classical approximation) can be used to calculate the redshift of a nearby object when spacetime is flat. However, many cases such as black holes and Big Bang cosmology require that redshifts be calculated using general relativity. Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; however, the resulting changes are distinguishable from true redshift and not generally referred as such (see section on physical optics and radiative transfer).
Read more about Redshift: History, Measurement, Characterization, and Interpretation, Redshift Formulae, Observations in Astronomy, Effects Due To Physical Optics or Radiative Transfer