Recall that alkenes undergo electrophilic addition. You may have seen this reaction in first semester organic in your alkene chapter.
Alkenes will form epoxides when reacted with a variety of peroxyacids.
The most common peroxy acids are meta-chloroperoxybenzoic acid (MCPBA) and peroxyacetic acid.
Recall that this process is stereospecific providing the syn addition products as a racemic mixture. Notice how the groups that were cis in the alkene are still cis in the product. The oxygen is added the the top and bottom faces to produce the two produce racemic mixture.
Recall that halohydrins are formed by treating alkenes with NBX/H2O or X2/H2O.
This is an example using NBS (N-bromosucciniimide) and water. Recall the anti addition forms a racemic mixture of enantiomers.
Treating halohydrins with a strong base yields the halohydrin.
This is also stereospecific and produces a racemic mixture analogous to using peroxyacids.