The increase of the yield stress vs. the magnetic field is the most important quantity characterizing the efficiency of a magnetorheological suspension. The theory based on the formation of columnar aggregates predicts a linear variation with the volume fraction of magnetic particles. In this paper we review previous models used to calculate forces and yield stress and will introduce a new model based on rupture at zero strain. Predictions of these models are compared with the experimental data obtained for carbonyl iron particles, by different authors. Whereas, previous analytical prediction strongly overestimates experimental yield stress, those calculated using the Finite Element Method (FEM), together with affine trajectories, reproduce the experiments well and show a linear dependence with the volume fraction and a H 3/2 behavior between 50 and 200 kA/m. Nevertheless, at very high-volume fractions (>55%), where the suspension can only flow in the presence of specific additives, the dependence of the yield stress vs. the volume fraction and the magnetic field is dramatically changed. We observed a jamming transition, which is triggered by the application of a low magnetic field and which depends strongly on the volume of the fraction. Here, we will discuss new perspectives arising from the use of these very high-volume fractions.