  Extraordinary magnetoresistance (EMR) is a geometric magnetoresistance effect
occurring in hybrid devices consisting of a high-mobility material joined by a
metal. The change in resistance can exceed 107% at room temperature when a
magnetic field of 5 T is applied. Magnetic field sensors based on EMR hold the
potential formeasuring weak magnetic fields with an unprecedented sensitivity,
yet, to date this potential is largely unmet. In this work, we provide an
extensive review of the current state-of-the-art in EMR sensors with a focus on
the hybrid device geometries, the constituent material properties and
applications of EMR. We present a direct comparison of the best devices in
literature across magnetoresistance, sensitivity and noise equivalent field for
different materials and geometric designs. The compilation of studies collected
in this review illustrates the extremely rich possibilities for tuning the
magnetoresistive behavior varying the device geometry and material properties.
In addition, we aim to improve the understanding of the EMR effect and its
interplay with geometry and material properties. Finally, we discuss recent
trends in the field and future perspectives for EMR.
