We will generalize the concept of partial and complete observables, intruduced by Rovelli, to constrained systems with an arbitrary number of (first class) constraints and to canonical field theories. Different methods to calculate complete observables (aka Dirac observables) will be presented and applied to examples, moreover their algebraic properties will be considered. Furthermore we will investigate whether it is possible to calculate complete observables in stages. In the case of gravity this will answer the question , whether it is possible to calculate the complete observable with respect to the Hamiltonian constraints, starting from 3-diffeomorphism invariant partial observables.