The Local Group of Galaxies was first recognized by Edwin P. Hubble and described in his The Realm of the Nebulae.
The Milky Way and the Andromeda Galaxy (also known as M31) are by far the most massive members of the Local Group and are considered the dominant members of the Group. The rest of the Group consists primarily of these two galaxies satellites, such as The Magellanic Clouds and many dwarf galaxies, though there are a number of members that are independent of the two dominant members.
The Local Group is actually spread in an approximate volume of ten million light years (sci.astro FAQ, Hartmut Frommert and Christine Kronberg) in diameter. Membership appears to be dynamic and has undergone significant change over time. There are currently approximately 30 members of the Local Group.
Many scientists are studying future scenarios for the Group, to give some indication of the fate of our home galaxy. The most common theories state that our galaxy and M31 will collide, creating a massive elliptical galaxy, and that the Local Group will eventually be "swallowed" by the almost incomprehensibly huge Virgo Supercluster of galaxies.
In addition, it appears that the Local Group is in gravitational interaction with at least four neighboring galactic groups.