Most of the universe is rushing away from us. It's not that we're particularly repellent; it's just that the universe is expanding, pushing most other galaxies away. Light from distant galaxies travels toward us through this expanding space, which stretches their light to longer, or redder, wavelengths. As a result, the spectra of most galaxies exhibit redshifts.
Now astronomers have accidentally discovered the greatest blueshift ever seen, in a star cluster that a giant black hole may have catapulted our way.
Over small distances gravity has reversed the universe's expansion, so modest blueshifts are common. Neither the solar system nor the galaxy is expanding. Not even the Local Group—the collection of approximately 75 galaxies that includes the Milky Way—expands. In fact, the Local Group's largest member, the Andromeda Galaxy, is moving toward us: it has a blueshift of 300 kilometers per second.