  Research on the exchange bias (EB) phenomenon has witnessed a flurry of
activity during recent years, which stems from its use in magnetic sensors and
as stabilizers in magnetic reading heads. EB was discovered in 1956 but it
attracted only limited attention until these applications, closely related to
giant magnetoresistance, were developed during the last decade. In this review
I first give a short introduction, listing the most salient experimental
results and what is required from an EB theory. Next, I indicate some of the
obstacles in the road towards a satisfactory understanding of the phenomenon.
The main body of the text reviews and critically discusses the activity that
has flourished, mainly during the last five years, in the theoretical front.
Finally, an evaluation of the progress made, and a critical assessment as to
where we stand nowadays along the road to a satisfactory theory, is presented.
