The classical boron Lewis acids, BX3, RBX2 and R2BX (X = F, C1, Br, I, OTf) are now popular tools in organic synthesis. B(II1) can act as a Lewis acid because there is an empty p-orbital on the boron. Enthalpy values indicate that when pyridine is the reference base, the Lewis acidity of Group IIIB halides increase in the order A1X3 > BX3 > GaX3. The Lewis acidity of BX3 generally increases in the order fluoride < chloride < bromide < iodide, i.e. the exact reverse of the order expected on the basis of the relative o-donor strengths of the halide anions. The main reason for this anomaly is that in these BX3 compounds, the B-X bonds contain a n-component which is formed by overlap of a filled p-orbital on the halogen with the empty p-orbital on the boron. Because the latter orbital is used to form an o-bond when BX3 coordinates with a Lewis base, this n-component is completely destroyed by complex formation. The strength of the n-component now increases in the order iodide < bromide < chloride < fluoride, i.e. the amount of n-bond energy that is lost on complex formation increases as the atomic weight of the halogen decreases. Evidently, as far as the extent of complex formation is concerned, this is a more important factor than the corresponding decrease in the o-donor strength of the halogen.The BF3 and BC13 complexes of diethyl ether are less stable than those of dimethyl ether, and the same order of stability is observed for the complexes of diethyl and dimethyl sulfides. As expected, steric interaction decreases as the distance between the metal and ligand atom is increased. Thus, it decreases when the metal atom is changed from boron to aluminum, or when the ligand atom is changed from oxygen to sulfur.The major applications of BX3 Lewis acids in organic synthesis include dealkylation of ethers, condensation reactions, and as a catalyst for Friedel-Crafts-type reactions and other acid-related chemistry. In general, these are used stoichiometrically in organic transformations under anhydrous conditions, because the presence of even a small amount of water causes rapid decomposition or deactivation of the promoters. To obviate some of these inherent problems, the potential of arylboron compounds, Ar,B(OH),-3 ( n = 1-3), bearing electron-withdrawing aromatic groups as a new class of boron catalysts has recently been demonstrated. For example, tris(pentafluor0phenyl)borane, B(C6F5)3, is a convenient, commercially available Lewis acid of strength comparable with that of BF3, but without the problems associated with reactive B-F bonds. Although its primary commercial application is as a co-catalyst in metallocene-mediated olefin polymerization, its potential as a Lewis acid catalyst for organic transformations is now recognized as being much more extensive. Diarylborinic acids and arylboronic acids bearing electron-withdrawing aromatic groups are also highly effective Lewis acid catalysts.This chapter focuses on the synthetic applications of BX3 as Lewis acids and the organic transformations catalyzed by arylboron...