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Miniaturized magnetic devices are ubiquitous in the hard disks of computers and in tape storage systems. Giant magnetoresistance was discovered as recently as 1988 but already sensors using the effect are being incorporated into read heads for the highest density hard disk systems. As a result of intensive research and development, storage density on hard disks has increased dramatically at a rate greater than 60% per year. At sub-micron and nano-scale dimensions the properties of magnetic devices are strongly affected by their size and shape in a complex way resulting from the interplay between different types of magnetic energy. In some cases this causes a deterioration in the performance of existing devices, however it has also enabled entirely new devices to be proposed. Arrays of nanomagnets could be used for ultra-high density storage on hard disks or for fast and dense, non-volatile, solid state memory. Storage applications are possible because hysteresis in the nanomagnets creates two oppositely magnetized states which are stable in zero applied field and can store binary data. Magnetic sensors based on giant magnetoresistance in layered magnetic structures are among the most sensitive available for operation at room temperature and above. This paper describes the physical properties of nanomagnets and their role in present and future applications.