In this work, based on a series of experiments conducted in recent and past years at the laser facility KI-1 of ILP SB RAS, approaches and main results on laboratory simulation of various explosive space plasma phenomena are presented. In a general perspective, the most important results have been obtained on the interaction of an expanding plasma cloud with a uniform magnetized background, on the dynamics of an exploding plasma in a dipole magnetic field and on the formation of an 'artificial magnetosphere' by a laser-produced plasma overflowing magnetic dipole. The last case corresponds to a possible extreme event of super compression of the Earth magnetosphere caused by a giant coronal mass ejection.