In property law of the United Kingdom and the United States and other common law countries, a remainder is a future interest given to a person (who is referred to as the transferee or remainderman) that is capable of becoming possessory upon the natural end of a prior estate created by the same instrument. Thus, the prior estate must be one that is capable of ending naturally, for example upon the expiration of a term of years or the death of a life tenant. A future interest following a fee simple absolute cannot be a remainder because of the preceding infinite duration.
For example, a person, D, gives ("conveys") a piece of real property called Blackacre "to A for life, and then to B and her heirs". A receives a life estate in Blackacre and B holds a remainder, which can become possessory when the prior estate naturally terminates (A's death). However, B cannot claim the property until A's death.
There are two types of remainders in property law: vested and contingent. A vested remainder is held by a specific person without any conditions precedent; a contingent remainder is one for which the holder has not been identified, or for which a condition precedent must be satisfied.
A remainder is vested if (1) the remainder is given to a presently existing and ascertained person, and (2) it is not subject to a condition precedent. A vested remainder may be indefeasibly vested, meaning that it is certain to become possessory in the future, and cannot be divested. An example, O conveys to "A for life, then to B and B's heirs." B has an "indefeasibly vested remainder" certain to become possessory upon termination of A's life estate. B or B's heirs will clearly be entitled to possession upon A's death. A vested remainder may not be certain to become possessory. An example of this: O conveys "to A for life, then to A's children." A has one child, B, so B has a vested remainder because B is ascertainable. But, A may have no other children in his life, and B could die before A, so the vested remainder is not certain to become possessory. Instead B is said to have a vested interest subject to partial (more children) and complete divestment (if B dies before A).
A remainder is contingent if one or more of the following is true: (1) it is given to an unascertained or unborn person, (2) it is made contingent on anything but the natural termination of the preceding estate.
For example, if we assume that B is alive, and O conveys "to A for life, then to the heirs of B...", then the remainder is contingent because the heirs of B cannot be ascertained until B dies. No living person can have actual heirs, only heirs apparent or heirs presumptive.
We might also assume that B is unmarried, and O conveys "to A for life, and then to B if B marries." B's interest is a contingent remainder because B's interest is contingent on B's getting married. 
The key difference between a reversion and a remainder is that a reversion is held by the grantor of the original conveyance, whereas "remainder" is used to refer to an interest that would be a reversion, but is instead transferred to someone other than the grantor. Similarly to reversions, remainders are usually created in conjunction with a life estate, life estate pur autre vie, or fee tail estate (or a future interest that will eventually become one of these estates).
Usage note: Although the term reversion is sometimes used to refer to the interest retained by a landlord when he grants possession to a tenant, not all real estate professionals can agree on the correctness of this usage of the term. Few people would refer to such a transferred interest as a remainder, so this type of "remainder" tends not to be a problem when discussing property rights.
In the United Kingdom it is possible for a patent creating a hereditary peerage to allow for succession by someone other than an heir-male or heir of the body, under a so-called "special remainder". Several instances may be cited: the Barony of Nelson (to an elder brother and his heirs-male), the Earldom of Roberts (to a daughter and her heirs-male), the Barony of Amherst (to a nephew and his heirs-male) and the Dukedom of Dover (to a younger son and his heirs-male while the eldest son is still alive). In many cases, at the time of the grant the proposed peer in question had no sons, nor any prospect of producing any, and the special remainder was made to allow remembrance of his personal honour to continue after his death and to preclude an otherwise certain rapid extinction of the peerage. However, in all cases the course of descent specified in the patent must be known in common law. For instance, the Crown may not make a "shifting limitation" in the letters patent; in other words, the patent may not vest the peerage in an individual and then, upon some event other than death (such as succession to a higher title), shift the title to another person. The doctrine was established in the Buckhurst Peerage Case (1876) 2 App Cas 1, in which the House of Lords deemed invalid the letters patent intended to keep the Barony of Buckhurst separate from the Earldom of De La Warr. The patent stipulated that if the holder of the barony should ever inherit the earldom, then he would be deprived of the barony, which would instead pass to the next successor as if the deprived holder had died without issue.