In writing for one of my never-to-see-the-light-of-day game universes, I had a reasoning behind undead.
Ordinary human beings contain spirits that control their metaphysique. Their attributes (Strength, Endurance, Reflexes, etc.) are a steady progression from physical to mental to metaphysical, with "Fortune" at the far end of metaphysique.
A human body is like a carrier that provides the necessary substance for a spirit to interact physically with the world. Ghosts and other apparitions are free spirits that can only affect the world metaphysically, meaning that they can instill emotions and feelings, can bless or curse those they encounter, and can cast spells. A spirit's power, aside from a small amount of energy which it draws from the "Supercosmos" automatically, is based on the number of people who are aware of its existence and believe in it. (This is the in-game justification for why people become depressed and ponder suicide when they are social outcasts.)
For a spirit to inhabit the body, however, it must be alive. The body must be able to breathe, pump blood, and otherwise to ensure that the spirit's essence is fully distributed throughout the body. If the body is not alive, it cannot carry the spirit's essence and the spirit leaves the body; it's a mutual dependence issue. When a being is conceived under the purview of a deity, one of the deity's followers' spirits is allowed to enter the body as its rightful spirit. Only during conception can a spirit assume control of a body, although if a body dies and a spirit leaves it, the rightful spirit can re-enter that body if the body is somehow resuscitated/resurrected -- though this requires the spirit to remain present and to choose to re-enter the body.
It is also possible for a body to be manipulated indirectly by a spirit, much like a puppet. This is what an undead being is. The body is very dead, but a spirit is very existent. The type of magic necessary to animate undead essentially involves seeking out a spirit roaming free in the Supercosmos and/or the mortal plane and asking it if it would like to control the body. More often than not, the spirit animating the body is not the rightful owner of the body, and has no recollection of any history or anything else to do with the body. The spirit often has motives of its own, so the person beseeching the spirit usually enters into some form of mutual contract that will accomplish the spirit's unfinished business in exchange for the undead's willing servitude. The "person" beseeching the spirit can also be a deity -- evil deities in particular will raise undead for no other reason than to kill living people so they have more spirits to enslave.
The more powerful the magic used, the more able the spirit is at controlling the body like a puppet. Zombies run the gamut from lumbering hulks to devastatingly fast and fearsome brutes. Because they feel no pain, the fastest zombies are easily the match of dozens of mortal men and can slaughter armies of living humanoids wholesale.
Do undead have souls? Yes, somewhere, off in the immortal plane. The souls that are controlling the bodies, however, are not the souls that belong there.
The more powerful forms of undead, e.g. revenants, are bodies that have been created from scratch or modified by hostile magic (usually evil deities) before being animated with a spirit.