The τ lepton magnetic moment theoretical predictions and measurements are reviewed. While it is believed that such a high mass particle is a good candidate to show up new physics, this is not the case up to now. The magnetic moment of elementary fermions, and in particular the anomalous magnetic moment of the electron, had an historical impact both in relativistic quantum mechanics and in quantum field theories. Besides, many new physics models were discarded when confronted with these magnitudes. More recently, the discrepancy of the experiments and the theoretical predictions for the muon anomalous magnetic moment is still an open issue. For the τ lepton, instead, while the theoretical prediction is well known for the standard model and some new physics models, the data are very far of determining even its sign or the first figure. We will discuss the most important theoretical aspects of the τ magnetic moment, and also the current accepted measurements and future perspectives, in particular related to B-factories.