Electron Pushing -- Acid Catalysis
Brønsted Acids: basically proton donors.
H3O+, H2SO4, HBr, HCl, H3PO4, etc
Lewis Acids: Neutral molecules or cations with a low lying vacant orbital. Often a metal with several electronegative ligands (F, Cl, Br, OTf, OAc, etc)
BF3, MgBr2, SnCl4, TiCl4, FeCl3, AlCl3, MeAlCl2, Me2AlCl, LiClO4, etc
Ag+ (special affinity for Cl, Br, I), Hg++ (special affinity for S, C=C, C≡C)
In addition to these inorganic Lewis acids, there are many chiral "designer" Lewis acids for initiating acid catalyzed reactions with asymmetric induction:
Related to Lewis acids are powerful alkylating (Me3O+ BF4- and MeOTf) or silylating (Me3SiOTf) agents which initiate similar chemistry, but the first step is a methyl or silyl transfer.
Bronsted and Lewis acids catalyze reactions by attaching to nucleophilic sites (lone pairs on O, N, S, π-bonds) in molecules, and activating the molecule to attack by nucleophiles. The equilibrium favoring the product cation (and thus the rate of subsequent reactions) is determined by the strength of the acid and the stability of the cation produced (among other factors).
Normally a positively charged atom is an electrophilic site only if it has a sextet of electrons or is otherwise electron deficient. Oxonium O and ammonium N atoms are not normally electrophilic centers. On the other hand, onium ions of the heavier elements (e.g., P, As, Se, Te, Br, I) are subject to nucleophilic attack.
Electrophilic catalysis is very closely related to oxidation.
Carbenium ions readily undergo rearrangement (Wagner-Meerwein)
Some named reactions which involve carbocation intermediates:
Friedel-Crafts Acylation and Alkylation,
Carbenium Ions with unusual properties
Common Stabilized Carbenium Ion Reaction Intermediates