A nearfield is an algebraic structure which satisfies all the field axioms except perhaps the left distributive law and commutativity of multiplication.

The finite sharply doubly transitive permutation groups are in one-to-one correspondence with the finite nearfields and several large classes of non-Desarguesian projective planes can be constructed from nearfields.

User-defined types will be available in the next release of Magma and in this talk I review some of the structure theory of nearfields and report on their implementation via user-defined types.