In this dissertation, the extraordinary magnetoresistance (EMR) effect in semiconductor/metal hybrid structures is studied to improve the performance in sensing applications. Using two-dimensional finite element simulations, the geometric dependence of the output sensitivity, which is a more relevant parameter for EMR sensors than the magnetoresistance (MR), is studied. The results show that the optimal geometry in this case is different from the geometry reported before, where the MR ratio was optimized. A device consisting of a semiconductor bar with length/width ratio of 5~10 and having only 2 contacts is found to exhibit the highest sensitivity. A newly developed three-dimensional finite element model is employed to investigate parameters that have been neglected with the two dimensional simulations utilized so far, i.e., thickness of metal shunt and arbitrary semiconductor/metal interface. The simulations show the influence of those parameters on the sensitivity is up to 10 %. The model also enables exploring the EMR effect in planar magnetic fields. In case of a bar device, the sensitivity to planar fields is about 15 % to 20 % of the one to perpendicular fields. 5 A “top-contacted” structure is proposed to reduce the complexity of fabrication, where neither patterning of the semiconductor nor precise alignment is required. A comparison of the new structure with a conventionally fabricated device shows that a similar magnetic field resolution of 24 nT/√Hz is obtained. A new 3-contact device is developed improving the poor low-field sensitivity observed in conventional EMR devices, resulting from its parabolic magnetoresistance response. The 3-contact device provides a considerable boost of the low field response by combining the Hall effect with the EMR effect, resulting in an increase of the output sensitivity by 5 times at 0.01 T compared to a 2-contact device. The results of this dissertation provide new insights into the optimization of EMR devices for sensor applications. Two novel concepts are presented, which are promising for realizing EMR devices with high spatial resolution and for opening new applications for EMR sensors in the low-field regime.