α-Halogenation of aldehydes and ketones is a reaction involving the substitution of α hydrogens with halogens in the presence of a base.  The reaction begins with the abstraction of  α hydrogen by the base to produce a nucleophilic enolate ion. This intermediate undergoes a subsequent nucleophilic substitution with the halogen to produce a monohalogenated carbonyl compound. If the starting substrate has more than one α hydrogen, it is difficult to stop the reaction...

Benzylic halogenation takes place under conditions that favor radical reactions such as heat, light, or a free radical initiator like peroxide.

Simple aryl halides do not react with nucleophiles. However, nucleophilic aromatic substitutions can be forced under certain conditions, such as high temperatures or strong bases. The mechanism of substitution under such conditions involves the highly unstable and reactive benzyne intermediate. Benzyne contains equivalent carbon centers at both ends of the triple bond, each of which is equally susceptible to nucleophilic attack. This 50–50 distribution of products is...

Halogenation is the addition of chlorine or bromine across the double bond in an alkene to yield a vicinal dihalide. The reaction occurs in the presence of inert and non-nucleophilic solvents, such as methylene chloride, chloroform, or carbon tetrachloride.
Consider the bromination of cyclopentene. Molecular bromine is polarized in the proximity of the π electrons of cyclopentene. An electrophilic bromine atom adds across the double bond, forming a cyclic bromonium ion intermediate.

SN2 substitutions and E2 eliminations of alkyl halides proceed via a concerted pathway. While the nucleophile attacks the alpha carbon in SN2 reactions, it functions as a strong base and abstracts a beta hydrogen in the E2 mechanism. The rate-limiting transition state in E2 elimination reactions is characterized by partially broken carbon–hydrogen and carbon–halogen bonds and a partially formed pi bond between the alpha and beta carbons. The beta hydrogen and halide are eliminated...

Electrophilic addition of hydrogen halides, HX (X = Cl, Br or I) to alkenes forms alkyl halides as per Markovnikov's rule, where the hydrogen gets added to the less substituted carbon of the double bond. Hydrohalogenation of alkynes takes place in a similar manner, with the first addition of HX forming a vinyl halide and the second giving a geminal dihalide.