An alkene, such as propene, reacts with bromine in the presence of water to yield a halohydrin. Halohydrins contain a halogen and a hydroxyl group attached to adjacent carbons. When the halogen is bromine, it is called a bromohydrin, while a chlorohydrin has chlorine as the halogen.

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.

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...

A method involving the transformation of methyl ketones to carboxylic acids using excess base and halogen is called the haloform reaction. It begins with the deprotonation of α hydrogen to form an enolate ion which reacts with the electrophilic halogen to give an α-halo ketone. The step continues until all the α protons are substituted to form a trihalomethyl ketone. The resulting molecule is unstable, and in the presence of a hydroxide base, it readily undergoes nucleophilic...

Malonic ester synthesis is a method to obtain α substituted carboxylic acids from ꞵ-diesters such as diethyl malonate and alkyl halides.

Overview
Epoxides result from alkene oxidation, which can be achieved by a) air, b) peroxy acids, c) hypochlorous acids, and d) halohydrin cyclization.
Epoxidation with Peroxy Acids
Epoxidation of alkenes via oxidation with peroxy acids involves the conversion of a carbon–carbon double bond to an epoxide using the oxidizing agent meta-chloroperoxybenzoic acid, commonly known as MCPBA. Since the O–O bond of peroxy acids is very weak, the addition of electrophilic oxygen of peroxy acids to...