Among the many different classes of stellar objects, neutron stars provide a unique environment where we can test (at the same time) our understanding of matter with extreme density, temperature, and magnetic field. In particular, the properties of matter under the influence of magnetic fields and the role of electromagnetism in physical processes are key areas of research in physics. However, despite decades of research, our limited knowledge on the physics of strong magnetic fields is clear: we only need to note that the strongest steady magnetic field achieved in terrestrial labs is some millions of Gauss, only thousands of times stronger than a common refrigerator magnet. In this general context, I will review here the state of the art of our research on the most magnetic objects in the Universe, a small sample of neutron stars called magnetars. The study of the large high-energy emission, and the flares from these strongly magnetized (~ 1015 Gauss) neutron stars is providing crucial information about the physics involved at these extremes conditions, and favoring us with many unexpected surprises.