It depends on whether you're referring to natural hair brushes, or synthetic.

For synthetic (which are normally used for liquid/cream makeup application), 91% isopropyl alcohol should be used to clean them thoroughly after each use. 91% isopropyl alcohol is inexpensive, and will not only remove all traces of makeup/oil, but will also kill any bacteria on the brush (plus, it evaporates very quickly, meaning the brush will dry a lot faster!) Do not use 91% isopropyl alcohol on natural hair brushes, as it will dry out the hairs and cause them to break off.

For natural hair brushes (which should only be used to apply powder makeup formulas), wipe them on an old (clean!) towel after every use to remove product. Then, wash once a week using mild shampoo, rinsing with clean, room temp water. That should remove any oils accumulating on the brush (which the brush may pick up from your face).

Whether natural hair or synthetic, ensure you prevent the ferrule of the brush (the part usually covered by metal, where the hairs are glued inside) from getting wet by either the alcohol, shampoo, or rinse water. Over time, it will break down the glue, and the hairs will begin to shed at an alarming rate, destroying the brush.