Stones are subdivided into two classes: chondrites and achondrites.

Chondrites get their name from the fact that they contain chondrules, tiny mineral spherules made mostly of silicates. Most chondrules are less than one millimeter across, although some may be as large as a few millimeters. In chondrites, chondrules are bound within a consolidated and fine-grained background matrix.

Chondrites are the most primitive meteorites known. That is, they are the most ancient ones in terms of when their constituents came together to form a rock, and the most unprocessed ones in terms of how little their materials have been altered since this rock formed. Chondrites are estimated to be approximately 4.5 million years old.

Achondrites make up about 10% of all stony meteorites. Achondrites lack chondrules and represent more processed materials. If Earth's surface rocks were meteorites, they would be achondrites, since they lack chondrules and are the result of extensive geological processing such as melting.

Chondrites, achondrites, stony-irons and irons are subdivided into groups and subgroups.

In addition, meteorites are divided into falls and finds depending on how they were collected.

Falls are meteorites whose arrival on Earth was witnessed and recorded. Their time of fall is thus relatively precisely known. These meteorites were usually recovered shortly after their arrival, although in the case of meteorite showers, additional fragments from a given fall may be recovered a long time after the fall occurred.

Falls give a reasonable estimate of the general population of meteorites reaching the Earth. The vast majority of falls are stones (92.8%), most of which turn out to be chondrites (85.7% of all falls). Irons are rare (5.7% of all falls); stony-irons rarer still (1.5%). In other words, by far most meteorites falling on Earth are chondrites.

Finds are meteorites that were not seen to fall but were subsequently discovered on the ground, often long after they landed. The time and circumstances of their arrival on Earth are thus not well documented. The vast majority of meteorites in museum and private collections around the world are finds, not falls. Stony meteorites tend to look like ordinary terrestrial rocks, especially if they were subjected to weathering, so they are easily overlooked. Stone finds are therefore rare in spite of the commonness of stones among falls. Finds in meteorite collections are instead dominated by irons, which not only have a distinctive appearance and are therefore easier to spot, but also resist weathering longer than stones and are easily found by metal detectors. Stony-irons would also be common among finds if it weren't for their lesser resistance to weathering compared to irons and, more importantly, for their extreme rarity among falls in the first place.

Meteorites, whether falls or finds, are usually given the name of the locality nearest the site where they were recovered. In cases where many meteorites are found within a relatively small area (such as Antarctica's blue ice fields), the meteorites are designated by locality name, sometimes abbreviated (the same name for all meteorites from that area) followed by a serial number. For Antarctic meteorites the year of find is also mentioned. ALH81005, for instance, is meteorite number 5 among those recovered in the Allan Hills area of Antarctica during the 1981-1982 field season.