Magnetoresistive materials are widely used for read-heads and are very good candidates for sensors due to their sensitivity. A large number of applications, at present covered by Hall sensors, can be targeted but they require having stable, reproducible, hysteresis-free and high signal-to-noise devices. This can be addressed by optimizing the material aspect (stack composition, magnetization direction) and the design. External biasing applied to giant magnetoresistance (GMR) sensors by integrated permanent magnets can be used to tailor the response and stabilize the sensor against random fields. In this paper, we present the work we have performed to tailor GMR samples to fulfill the requirements of two specific applications. In the first case we have developed very stable and reproducible current sensors with the aim of permanent magnet biasing. In the second case we show results on a single-chip 2D compass, where the Earth's field measurement is obtained by a local magnetization reversal of the hard layer. The sensitivity of this compass is 3° for a current consumption of 200 μA.