A resulting trust (from the Latin 'resultare' meaning 'to jump back') is a situation where property "results" back to the transferor. In this instance, the word 'result' means "in the result, remains with", or something similar to "revert" except that in the result the beneficial interest is held on trust for the settlor. Not all trusts whose beneficiary is also its settlor can be called a resulting trust. In common law, the resulting trust refers to a subset of trusts which have such outcome; express trusts which stipulate that the settlor is to be the beneficiary are not normally considered resulting trusts.
The beneficial interest results in the settlor, or if the settlor has died the property forms part of the settlor's estate.
In US law, if there is a close personal relationship between the parties a gift is presumed rather than a trust creating a rebuttable presumption (typically between sibling, uncles, aunts, children, grandchildren, but not the husband or wife).
If the title holder's take for an illegal purpose, then there is no implication of a trust, however, where the wrongdoing is outweighed by unjust enrichment by the other party, a trust may be created.
One attempt to classify resulting trusts was made by Megarry J in Re Vandervell's Trusts (no.2) Ch 269. According to Megarry J there are two sorts of resulting trusts in English law.
Presumptive resulting trusts
These are transfers made by A to B, where the law creates a rebuttable presumption of a resulting trust applying if the intention is not made clear by A.
For example, when A transfers property to B, unless the transfer was made by father to child or by husband to wife, in the absence of any other evidence the law presumes that a resulting trust has been created for A.
The main categories of fact situations giving rise to a presumption of a resulting trust are: - Where A makes a voluntary conveyance of property to B - Where A has made a monetary contribution to the purchase of property for B (The Venture,  P 218,(1907) 77 L.J.P. 105.)
The presumptions are, however, easily rebutted. In Fowkes v Pascoe (1875) LR 10 Ch App 343, evidence was shown that a woman had purchased stock in the names of herself and her grandson; evidence by the grandson and grand-daughter-in-law that this had been done as a gift was admissible. On the other hand, the presumption is solely concerned with evidence of an intent to create a trust; ulterior motives to create a trust are not taken into account. In Tinsley v Milligan  1 AC 340, a woman transferred property to her lover on trust in order to fraudulently claim social security payments; it was held that this did not defeat the presumption of a resulting trust.
The fact that is being proved by the presumption of a resulting trust is the intention to create a trust for the settlor. This view of presumed resulting trusts has been endorsed by Lord Browne-Wilkinson in (Westdeutsche landesbank v council of london borough of islington  AC 669);
"...the presumption of resulting trust is rebutted by evidence of any intention inconsistent with such a trust, not only by evidence of an intention to make a gift."
Some have argued that this presumption arises as a result of a lack of intention to transfer any beneficial interest,. This view has generally not received judicial endorsement.
Presumptions of resulting trust, especially in the context of husband-to-wife transfers, have been criticised as anachronistic. In Pettitt v Pettitt 1970 AC 777, Lord Diplock observed that
"It would, in my view, be an abuse of the legal technique for ascertaining or imputing intention to apply to transactions between the post-war generation of married couples "presumptions which are based upon inferences of fact which an earlier generation of judges drew as to the most likely intentions of earlier generations of spouses belonging to the propertied classes of a different social era."
Automatic resulting trusts
In these trusts " there is no mention of any expression of intention in any instrument, or of any presumption of a resulting trust: the resulting trust takes effect by operation of law, and so appears to be automatic." (per Megarry J, Re Vandervell's Trusts (no.2)) 
Automatic resulting trusts can arise when the settlor tries to set up a trust for a third party, but there is an initial failure for want of objects; for example, by naming beneficiaries which cannot be defined, as in Morice v Bishop of Durham 1805 10 Ves 522, or when the objectives of the trust no longer become possible or relevant by the time of the transfer to the trustee, as in Re Gillingham Bus Disaster Fund  Ch 300.
In relation to automatic resulting trusts, there is some difference in expressing the nature of the settlor's intention:
Although in many cases the outcome would be the same, the difference is significant. It is often difficult to prove intention, but easier to prove the circumstances when a legal presumption will arise. It may be more or less easy to rebut a presumption than to disprove an intention.
Lord Browne-Wilkinson was afraid that this would create a "floodgates" problem, by giving every claimant a proprietary right in bankruptcy - making many more claimants secured creditors, and thus making the position of a secured creditor much less valuable.
In South Africa there is no doctrine of resulting trusts. The main remedy if any of the trust purposes should fail would be through Unjust enrichment. (westdeutsche landesbank v council of london borough of islington)