Friedel-Crafts reactions involve the use of Friedel-Crafts catalysts to alkylate or acylate an aromatic ring - this necessitates the formation of a carbon-carbon bond onto an aromatic ring, which is synthetically very useful, and otherwise difficult to achieve. The two reaction types are best dealt with separately;

Alkylation

The commonly used reagent for this is an alkyl halide (alkyl halides are electrophilic, but not enough to react with the stable aromatic system) activated by a Lewis Acid - like those used in halogenation. Here is an example of the reaction mechanism;

A range of possible Lewis Acids is shown below, in order of how effective they are in the Friedel-Crafts reaction;

SnCl₄ < ZnCl₂ < TiCl₃ < BF₃ < FeCl₃ < AlCl₃

A pitfall of this mechanism is that rearrangement of the alkyl group can often occur, if a more stable carbocationic structure is available - suggesting that the polarisation of the alkyl halide is such that the alkyl part does have carbocationic character. This is a thermodynamic phenomenon (the notion of something being more 'stable' is a thermodynamic one), so under thermodynamic conditions (higher temperature) more rearrangement will occur. An example of the possible rearrangement is shown here;

Another thing to be wary of is that aromatic rings that are electron deficient (i.e. have EWGs attached) are deactivated to this and all kinds of electrophilic reactions - so for example nitrobenzene will not Friedel-Crafts alkylate.

Acylation

Acylation is the addition of a carbonyl group to an aromatic ring - usually to form a ketone. The reagent of choice is an acid halide (see here), activated (even a molecule as reactive as an acid halide needs to be activated in order for it to react with an aromatic ring!) using the same Lewis Acids as alkylation;