This paper makes a brief review on 30 years of history of the wind power short-term prediction, since the first ideas and sketches on the theme to the actual state of the art on models and tools, giving emphasis to the most significant proposals and developments. The two principal lines of thought on short-term prediction (mathematical and physical) are indistinctly treated here and comparisons between models and tools are avoided, mainly because, on the one hand, a standard for a measure of performance is still not adopted and, on the other hand, it is very important that the data are exactly the same in order to compare two models (this fact makes it almost impossible to carry out a quantitative comparison between a huge number of models and methods). In place of a quantitative description, a qualitative approach is preferred for this review, remarking the contribution (and innovative aspect) of each model. On the basis of the review, some topics for future research are pointed out