A first screen for what is patentable subject matter is the wording of section 101 of the Patent Act, which requires a "new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof." This language excludes what one might call a "useless" idea or theory, but to the extent an idea or theory can be both new and useful, and to the extent it is embodied in a machine, manufacture, or so forth, it passes this threshold.
The Supreme Court, in a line of precedents going back to 1852, has long held that "abstract" ideas are not patentable. In the case it heard that year, the patent holder claimed as its invention a certain combination of techniques used to create pipes out of lead. In the course of a wide-ranging discussion, the court said: "A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented...."
More Recent Application
What ideas are too abstract to be patentable remains a commonly litigated issue in the 21st century. In 2010, the Supreme Court decided against two men (Bilski and Warsaw) who had together filed a patent application on a method of hedging risk in the purchase of energy-related commodities such as coal or natural gas. The court said that this was a mere abstract idea.
Few Bright Lines
The Supreme Court's Bilski decision didn't give any definitive test for abstractness, and it specifically rejected some possible bright-line standards. For example, it would not say that "business methods" in general cannot be patented. The statute "leaves open the possibility that there are at least some processes that can be fairly described as business methods that are within patentable subject matter under section 101." Though there are still few bright lines, the general trend in recent years has been toward a narrower understanding of what is patentable, a broader understanding of some of the doctrinal limits such as the exclusion of abstract ideas.
Laws of Nature
A related idea is that "laws of nature" are not subject to patent. For example, it is an observed fact that the human body metabolizes certain substances in a predictable way. Nobody can own that regularity/law. No one, then, can enforce a patent for a medical procedure that consists entirely of observing the effects of that regularity.