Basic concepts and notions of orthogonal representations are in-troduced. If X : G → GL(V ) is a K-representation of a nite group G it may happen that its image X(G) xes a non-degenerate quadratic form q on V . In this case X and its character χ : G → K, g 7 → trace(X(g)) are called orthogonal. If χ is an irreducible orthogonal character of even degree this form is unique up to scalars and there is a unique square class detχ in the character eld Q(χ) = Q(χ(g) | g ∈ G) such that given any eld L with a representation that aords χ, the determinant of the xed form q is det(q) = detχ(L×)2. In this talk we will discuss computational methods for determining this square class which is called the orthogonal determinant of χ. We will also briey mention theoretical tools for determining this square class.