Epoxides experience a great deal of ring strain and as such are rather reactive. They undergo ring-opening reactions under acidic or basic/nucleophilic conditions.
In acid catalyzed ring-opening the epoxide oxygen is protonated under acidic conditions, activating it for nucleophilic attack.
For example treating ethylene oxide with H-X proceeds by the following mechanism.
Millions of tons of ethylene glycol are produced by the following method which undergoes a similar mechanism.
Alcohols can also behave as nucleophiles under acidic conditions, resulting in ethers.
For unsymmetrical epoxides it depends on the structure of the epoxide.
If one side is primary and one side is secondary, then the reactions proceeds in an SN2 fashion
If however one side is tertiary then it proceeds as though is were SN1.
Some have proposed a structure for the protonated epoxide that looks more like tertiary cation. Note that the sterochemistry is still maintained, so a discrete cation does not form,