Relations are ways in which several entities stand to each other. They usually connect distinct entities but some associate an entity with itself. The adicity of a relation is the number of entities it connects. The direction of a relation is the order in which the elements are related to each other. The converse of a relation carries the same information and has the opposite direction, like the contrast between "two is less than five" and "five is greater than two". Both relations and properties express features in reality with a key difference being that relations apply to several entities while properties belong to a single entity.

Many types of relations are discussed in the academic literature. Internal relations, like resemblance, depend only on the monadic properties of the relata. They contrast with external relations, like spatial relations, which express characteristics that go beyond what their relata are like. Formal relations, like identity, involve abstract and topic-neutral ideas while material relations, like loving, have concrete and substantial contents. Logical relations are relations between propositions while causal relations connect concrete events. Symmetric, transitive, and reflexive relations are distinguished by their structural features.

Metaphysical difficulties like the question of where relations are located lie at the center of discussions of their ontological status. Eliminativism is the thesis that relations are mental abstractions that are not a part of external reality. A less radical position is reductionism, which claims that relations can be explained in terms of other entities, like monadic properties, and are not a substantial addition to reality. According to realists, relations have a mind-independent existence. A strong form of realism is relationalism, which states that all of reality is relational at its most basic level. Historically, eliminativism and reductionism were the dominant views. This only changed toward the end of the 19th century, when various developments in the fields of mathematics, logic, and science prompted a more realist outlook.

A relation is a manner in which multiple entities stand to each other. It is a connection or association between entities and can be understood as a feature characterizing these entities as a whole. Many relations hold between distinct entities. For example, the first-born sibling stands in the relation of being older than to their other siblings. But an entity can also stand in a relation to itself. For instance, every entity stands in the relation of identity to itself. Relations can hold between diverse entities, including objects, people, and concepts. If a relation holds between entities then the relation together with the entities constitutes a fact or state of affairs.

The word "relationship" is often used as a synonym. The entities related to each other are called the relata. The term "relation" comes from the Latin terms relatio and referre, which mean reference or towardness.

In mathematics and logic, relations are defined as set-theoretic structures. For example, the relation less than is defined as the set of all ordered pairs in which the first element is less than the second element. This set includes pairs like [1,2], [1,3], and [2,17]. Mathematical functions are a special type of relation in which one or several elements are uniquely associated with exactly one other element.

Relations have various characteristic features, like the number of relata they have and the direction in which they connect them. They are closely associated with properties and share several aspects with them.

The adicity of a relation is the number of places or relata it has. The terms "arity" and "degree" are used as synonyms. For instance, the relation being larger than has an adicity of two since it involves two entities: a smaller entity and a larger entity. Another example is the relation of being adjacent to. Relations with an adicity of two are called dyadic or binary. Triadic or ternary relations have an adicity of three, like the relation of giving, which involves a giver, a receiver, and a given object. The relation of being between is also triadic since it requires two entities on the sides and one in the middle, as in "5 is between 2 and 23".