Giant Magnetoresistances (GMR) and Tunnel Magnetoresistances (TMR) take an increasing part in many applications like current sensing, magnetometry or position sensing, thanks to their high magnetoresistance at room temperature, which leads to a large output signal variation. But the real performances of such sensors can only be estimated with respect to the sources of noise. In this chapter, we give first some bases on noise theory and data treatment. Fluctuations, ergodicity and volume considerations will be discussed. A second part will detail noise measurement techniques and data analysis of typical noise power spectra. Sources of noise will be discussed in a third part. In the end of the chapter, specific cases of GMR and TMR magnetic noise and non magnetic noise will be discussed with their physical origin and their analytical or phenomenological expression. We will then present ways to design GMR and TMR sensors for noise reduction, depending on the applications targeted.