The expansion of the universe makes measuring the distance to distant objects complicated. Rather than using distance units, astronomers measure the redshift (z) of distant objects such as galaxies. z corresponds to the number of years the light from an object has traveled to reach us. This is not the distance to the object in light years, however, because the universe has been expanding as the light traveled and the object is now much farther away. The more distant an object, the more it will be redshifted. Some very distant objects may emit energy in the ultraviolet or even higher energy wavelengths. As the light travels great distances and is redshifted, its wavelength may be shifted by a factor of 10. So light that starts out as ultraviolet may be become infrared by the time it gets to us!
The highest known redshifts are from galaxies producing gamma ray bursts. The highest confirmed redshift is for a galaxy called UDFy-38135539 with a z value of 8.6, which corresponds to a light travel time of about 13.1 billion years. This means the light we see now left the galaxy about 600 million years after the Big Bang! The galaxy is now 30.384 billion light years away from us due to the expansion of the universe during the time the light from the galaxy traveled to us.
As the universe expands, the space between galaxies is expanding. The more distance between us and a galaxy, the more quickly the galaxy will appear to be moving away from us.
It is important to remember that although such distant galaxies can appear to be moving away from us at near the speed of light, the galaxy itself is not traveling so fast. Its motion away from us is due to the expansion of the space between us.