The purpose of this paper is to study hyperelliptic curves with extra involutions. The locus Lg of such genus-g hyperelliptic curves is a g-dimensional subvariety of the moduli space of hyperelliptic curves Hg. The authors present a birational parameterization of Lg via dihedral invariants, and show how these invariants can be used to determine the field of moduli of points p ∈ Lg. They conjecture that for p ∈ Hg with |Aut(p)| > 2, the field of moduli is a field of definition, and they prove this conjecture for any point p ∈ Lg such that the Klein 4-group is embedded in the reduced automorphism group of p. Further, for g = 3, they show that for every moduli point p ∈ H3 such that |Aut(p)| > 4, the field of moduli is a field of definition. A rational model of the curve over its field of moduli is provided.