Formation of enols and enolates
Aldehydes and ketones have acidic hydrogens on the $\alpha$ carbon, which can be removed using strong bases, forming resonance-stabilized enolate ions.
Alkylation of enolate ions
Enolate ions are alkylated by attacking carbon electrophiles such as haloalkanes, epoxides, other carbonyls, etc.
Halogenation of aldehydes and ketones
The $\alpha$ position of aldehydes and ketones is halogenated through enol or enolate intermediates.
Hydrogen - Deuterium Exchange
Aldol condensation
Aldehydes and ketones undergo base-catalyzed condensations in which the enolate of one molecule attacks the carbonyl of another. This reaction is known as the aldol condensation.
Preparation of a,b-unsaturateds
Michael and Robinson
Enolates also attack $\alpha,\beta$-unsaturated carbonyls, forming 1,5-dicarbonyl compounds that can subsequently condense via an intramolecular aldol reaction. These are known as the Michael and Robinson reactions.