A stereocenter consists of an atom holding a set of ligands (atoms or groups of atoms) in a spatial arrangement which is not superposable on its mirror image. A chiral center is a generalized extension of an asymmetric carbon atom, which is a carbon atom bonded to four different entities, such that an interchanging of any two groups gives rise to an enantiomer.  In organic chemistry a chiral center usually refers to a carbon, phosphorus, or sulfur atom, though it is also possible for other atoms to be chiral centers in organic and inorganic chemistry.
The term stereocenter was introduced in 1984 by Mislow and Siegel.
Possible number of stereoisomers
A molecule can have multiple stereocenters, giving it many stereoisomers. In compounds whose stereoisomerism is due to tetrahedral stereogenic centers, the total number of hypothetically possible stereoisomers will not exceed 2n, where n is the number of tetrahedral stereocenters. Molecules with symmetry frequently have fewer than the maximum possible number of stereoisomers.
Having two chiral centers may give a meso compound which is achiral. Certain configurations may not exist due to steric reasons. Cyclic compounds with chiral centers may not exhibit chirality due to the presence of a two-fold rotation axis. Planar chirality may also provide for chirality without having an actual chiral center present.
A chiral carbon or asymmetric carbon is a carbon atom which is asymmetric. Most chiral molecules have a chiral carbon, though the presence of a chiral carbon does not necessarily make a molecule chiral (see meso compound). A chiral carbon is often denoted by C*.
If the carbon is chiral, it follows that:
- the carbon atom is sp3-hybridized;
- there are four different groups attached to the carbon atom.
Almost any other configuration for the carbon would produce a center of symmetry. For example, an sp- or sp2-hybridized molecule would be planar, with a mirror plane. Two identical groups would give a mirror plane bisecting the molecule.
Other chiral centers
Chirality is not limited to carbon atoms, though carbon atoms are often centers of chirality due to their ubiquity in organic chemistry.
Nitrogen and phosphorus atoms are also tetrahedral. Racemization by Walden inversion may be restricted (such as ammonium or phosphonium cations), or slow. This allows the presence of chirality.
Metal atoms with tetrahedral or octahedral geometries may also be chiral due to having different ligands. For the octahedral case, several chiralities are possible. Having three ligands of two types, the ligands may be lined up along the meridian, giving the mer-isomer, or forming a face — the fac isomer. Having three bidentate ligands of only one type gives a propeller-type structure, with two different enantiomers denoted Λ and Δ.
- Cahn–Ingold–Prelog priority rules for nomenclature