Magnetoimpedance (MI) in amorphous wires is widely used for the development of various sensors and smart composites with sensing functionalities. In the case of sensor applications, MI in off-diagonal configuration has a number of advantages including linearity, enhanced output voltage sensitivity, efficient resonance, or differential excitation schemes. In this article, we discuss the fundamentals of the off-diagonal MI in amorphous microwires, working principles, and design of miniature MI magnetic sensors. Considering the electrodynamic origin of MI, a comparison with orthogonal fluxgates is made with the purpose to suggest improvements in MI sensor design. This includes multi-wire configuration and suppression of the voltage offset caused by magnetic anisotropy helicity. New results on the heating effects reveal that the temperature stability along with sensitivity may be enhanced by annealing. The paper focus is aimed to demonstrate that the off-diagonal MI sensors have a high potential for improvements in terms of output voltage sensitivity, magnetic field resolution and temperature stability. 1 Introduction The magnetoimpedance (MI) in soft magnetic conductors demonstrating a very high sensitivity over a wide range of operating frequencies has been recently employed for the development of miniature sensors to detect extremely low magnetic fields, for example, the fields generated by electrical processes of the human heart (MCG [1, 2]). The MI effect includes an enormous change in the high frequency voltage across a magnetic conductor caused by the application of low magnetic fields in the range of few Oersted. In this respect, it can be compared with giant magnetoresistance but high operating frequencies require completely different MI sensor construction. It appears that a simple scheme of measuring the voltage across the MI material involves a number of difficulties associated with nonlinear MI characteristics and relatively low output voltage sensitivity. This scheme, however, is successfully used with thin-film MI materials combined with permanent magnetic layers to shift the operating field point [3-5].