I summarize recent results from large scale Monte Carlo simulations of scalar O(4) theory in the broken phase. The wave function renormalization constant ZG, the mass of the scalar particle mσ and the scalar field expectation value Σ are determined. The effect of the finite lattice size on the scalar mass is estimated. The upper bound on the ratio mσ/ fG is 2.6(1) at a value of the cut-off Λ cut⋍2.5 , corresponding to an triviality bound of 8.2(5) on the ratio of the Higgs mass over W mass. First results of an extensive calculation on various lattice sizes at finite small external source j and at a value of f G ⋍ .4 are presented. Taking into account the effect of the Goldstone states via analytic formulae, the scalar field expectation value Σ is determined. The agreement of this value calculated at finite j and the calculation using rotates fields at j=0 is impressive.