Fields are typically sets of “numbers” in which the arithmetic operations of addition, subtraction, multiplication and division are defined. The following is a list of examples of fields.

• The set of all rational numbers , all real numbers and all complex numbers are the most familiar examples of fields.
• Slightly more exotic, the hyperreal numbers and the surreal numbers are fields containing infinitesimal and infinitely large numbers. (The surreal numbers aren't a field in the strict sense since they form a proper class and not a set.)
• The algebraic numbers form a field; this is the algebraic closure of . In general, every field has an (essentially unique) algebraic closure.
• The computable complex numbers (those whose digit sequence can be produced by a Turing machine) form a field. The definable complex numbers (those which can be precisely specified using a logical formula) form a field containing the computable numbers; arguably, this field contains all the numbers we can ever talk about. It is countable.
• The so-called algebraic number fields (sometimes just called number fields) arise from by adjoining some (finite number of) algebraic numbers. For instance and (every separable finite field extension is simple).
• If is a prime number, then the -adic numbers form a field which is the completion of the field with respect to the -adic valuation.
• If is a prime number, then the integers modulo form a finite field with elements, typically denoted by . More generally, for every prime power there is one and only one finite field with elements.
• If is a field, we can form the field of rational functions over , denoted by . It consists of quotients of polynomials in with coefficients in .
• If is a variety over the field , then the function field of , denoted by , consists of all quotients of polynomial functions defined on .
• If is a domain (= connected open set) in , then the set of all meromorphic functions on is a field. More generally, the meromorphic functions on any Riemann surface form a field.
• If is a variety (or scheme) then the rational functions on form a field. At each point of , there is also a residue field which contains information about that point.
• The field of formal Laurent series over the field in the variable consists of all expressions of the form
  
  where is some integer and the coefficients come from .
• More generally, whenever is an integral domain, we can form its field of fractions, a field whose elements are the fractions of elements of .

Many of the fields described above have some sort of additional structure, for example a topology (yielding a topological field), a total order, or a canonical absolute value.