Electrophilic addition proceeds by two slightly different mechanisms, according to whether the electrophile has an unshared pair (halogen, mercury, oxygen) or not (proton, boron):
In the first case, the nucleophilic part of the reagent attacks the more substituted end of the bridged ion; this gives the same regioselectivity as the pathway through a carbocation. Note that the former case results in anti- addition, whereas the latter case is not stereoselective because of the planarity of the carbocation intermediate.
Either way, the initial interaction is a "filled-empty" interaction between the filled p orbital of the double bond, and the s* orbital of the X-X or H-X bond.
The number of possible electrophiles is quite large. Some examples:
If the reaction is conducted in a nucleophilic solvent, products from attack of the solvent on the intermediate -onium ion will be observed.