In January 1979, for the first time, recurrent short (<100ms) and intense gamma-ray bursts were detected from a source in the direction of the Galactic center, later named SGR1806-20. Two months later, in March 1979, rapid coherent X-ray pulsations were discovered during an intense flare from SGR0506-66, the prototype of the magnetar class. Since then, many advances have been achieved in the study of this class of high energy emitting isolated neutron stars, thought to shine in the X-rays due to the decay of the strongest magnetic fields present in the Universe (> 10^15 Gauss). The results obtained through the study of the transient phenomena displayed by some of them over more than 10 orders of magnitudes of time scale variability (from fraction of milli-seconds up to years) and of flux (from 10^-9 up to 1 ergs/s/cm^2) will be shown and discussed, with particular emphasis on the most recent results obtained. Among others are: the discovery of rapid QPOs in the giant flares of SGR1806-20 and SGR1900+14, the study of intermediate flares from SGR1900+14 and 1E1547.0- 5408, and the detection of long-duration outbursts from transient Anomalous X-ray Pulsars (XTE J1810−197, CXO J164710.2−455216 and 1E1547.0-5408) monitored through multi-wavelength observations. Information related to the neutron star and magnetosphere structure, the emitting processes, and the confined fireball properties have been inferred and will be discussed on the light of the theoretical model(s).