There are two types of halogenation.
An example is the addition of bromine to ethene.
Halogens react with alkanes under the influence of heat or light to form alkyl halides.
The halogen atom replaces a hydrogen atom in the alkane, so this is a substitution reaction.
Aromatic compounds undergo halogen substitution reactions in the presence of Lewis acids.
Here's a video on the halogenation of alkanes.