Over many years, we developed the construction of the ϕ4-model on four-dimensional Moyal space. The solution of the related matrix model Z[E,J]=∫dΦexp(tr(JΦ−EΦ2−λ4Φ4)) is given in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of E. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. Locality is fulfilled. The Schwinger 2-point function is reflection positive in special cases.