Non-coordinating ion
Anions that interact weakly with cations are optimistically termed non-coordinating anions, although a more accurate term is 'weakly coordinating anion'. Non-coordinating anions are useful in studying the reactivity of electrophilic cations.  They are commonly found  as counterions for cationic metal complexes with an unsaturated coordination sphere.  These special anions are essential components of homogeneous olefin polymerisation catalysts, where the active catalyst is a coordinatively unsaturated, cationic transition metal complex.  For example, they are employed as counterions for the 14 valence electron cations + (R = methyl or a growing polyethylene chain).

# Pre-"BARF" era
Prior to the 1990s, BF4, PF6, and  ClO4 were considered weakly-coordinating anions.  These species are now known to bind well to electrophilic metal centers.  A particular problem inhibits the use of ClO4, as its salts with organic cations are sometimes explosive.  For this reason, perchlorate has almost fallen out of use due to safety concerns.  Tetrafluoroborate and hexafluorophosphate anions are coordinating toward highly electrophilic metal ions, such as cations containing Zr(IV) centers, which can abstract fluoride from these anions.
Other anions wee considered as low-coordinating with many cations, e.g., triflates for high-temperature applications.

# Era of BARF
A revolution in this area occurred in the 1990s with the introduction of 4], commonly abbreviated as  and affectionately called "BARF.". This anion is far less coordinating than the tetrafluoroborate BF4, hexafluorophosphate PF6, and perchlorate ClO4, consequently it has enabled the study of still more electrophilic cations.
File:NoncoordAnNew.png
In the tetraarylborates, the negative charge is symmetrically distributed over many electronegative atoms. Related anions are derived from tris(pentafluorophenyl)boron.  Another advantage of these anions is that their salts are more soluble in non-polar organic solvents such as dichloromethane and, in some cases, even alkanes.  Polar solvents, such as acetonitrile, THF, and water tend to bind to electrophilic centers, in which cases, the use of a noncoordinating anion is pointless.
Two publications describe pioneering results on "BARF"
- The first preparation of B4:
Nishida, H.; Takada, N.; Yoshimura, M.; Sonods, T.; Kobayashi, H. Bulletin of the Chemical Society of Japan 1984, volume 57, pp. 2600.
- The preparation of 2]+B4:Brookhart, M.; Grant, B.; Volpe, Jr., A. F.; Organometallics. 1992, volume 11, pp. 3920-3922.doi:10.1021/om00059a071.

# Uses of non-coordinating anions
Complexes derived from noncoordinating anions have been used to catalyze hydrogenation, hydrosilylation, oligomerization, and the living polymerization of olefins.  The popularization of non-coordinating anions has contributed to increased understanding of agostic complexes wherein hydrocarbons and hydrogen serve as ligands.
The first example of a three-coordinate silicon compound was generated using a non-coordinating anion.  Specifically, the salt   contains a noncoordinating anion derived from a carborane. 
Noncoordinating anions are important components of many superacids, which result from the combination of Bronsted acids and Lewis acids.

# Related Lewis acids
The neutral molecules that represent the parents to the non-coordinating anions are generally strong Lewis acids, e.g. boron trifluoride, BF3 and phosphorus pentafluoride, PF5.  Perhaps the most notable Lewis acid of this genre is B(C6F5)3.