Cleavage at met-x bonds by cyanogen bromide

Electrophilic addition of halogens to alkenes proceeds via a cyclic halonium ion to form a 1,2-dihalide or a vicinal dihalide.

Alkynes undergo oxidative cleavage in the presence of oxidizing reagents like potassium permanganate and ozone. The triple bond — one σ bond and two π bonds — is completely cleaved, and the alkyne is oxidized to carboxylic acids. When warm and basic aqueous potassium permanganate is used as an oxidizing agent, alkynes are first converted to carboxylate salts via an unstable α-diketone intermediate. Further, a mild acid treatment protonates the carboxylate anions generating free carboxylic acid...

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.

A bond is formed between two atoms by sharing two electrons. When this bond is broken by supplying sufficient energy, either two electrons can be taken up by one atom forming ions by the cleavage called heterolysis, or the two electrons are shared by two atoms, with one each creating radicals by the cleavage called homolysis.