Recently, many type systems for records have been proposed. For most of them, the types cannot be describes as the terms of an algebra. In this case, type checking or type inference in the case of first order type systems, cannot be derived from existing algorithms. We define record terms as the terms of an equational algebra. We prove decidability of the unification problem for records terms by showing that its equational theory is syntactic. We derive a complete algorithm and prove its determination. We define a notion of canonical terms and approximations of record terms by canonical terms, and show that approximations commute with unification. We also study generic record terms, which extend record terms to model a form os sharing between terms. We prove that the equational theory of generic record terms and that the corresponding unification algorithm always terminates.