This paper revisits a model for elliptic curves over Q introduced by Huff in 1948 to study a diophantine problem. Huff's model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of Z/4Z x Z/2Z is birationally equivalent to a Huff curve over the original field. This paper extends and generalizes Huff's model. It presents fast ex- plicit formulae for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the so-obtained formulae feature some useful properties, including completeness and independence of the curve parameters.