Neutron stars are by far the strongest known magnets in the universe. Some of them (called magnetars) generate explosions by suddenly dissipating magnetic energy with a rate up to $10^{47}$ erg/s. These magnetic explosions emit giant gamma-ray flares observed in our and neighboring galaxies. Similar explosions in distant galaxies are proposed as the engines of the mysterious fast radio bursts (FRBs). Yet more powerful energy release occurs when two neutron stars merge. These cataclysmic events produce gravitational waves, neutrinos, and bright electromagnetic emission. Both mergers and isolated magnetar flares involve ultra-strong magnetic fields of $10^{15}-10^{16}$ G, sudden heating to MeV temperatures, creation of copious electron-positron pairs, and launching of ultra-relativistic outflows and shock waves. Recent numerical experiments shed light on the extreme plasma physics in these events, in particular the dissipation mechanisms releasing the observed energy. Observations and simulations of the ultra-powerful bursts also provide insights into neutron star interior. 

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