PACS 75.50.Gg, 75.50.Xx Ultrahigh magnetic fields (B = 100 -1000 T) are valuable means for many-sided research in solid state physics. A brief description of the explosion method and some results of its application are presented. The magnetic coil compensation method has been used to study the first order phase transitions in a broad range of fields and temperatures. The Faraday rotation method has been applied to measure the second order magnetic phase transitions. A number of magnetic materials were studied experimentally and theoretically: first order phase transitions in RCo 2 compounds, second order transitions in KMnF 3 , MnF 2 , etc. and steplike quantum magnetization process (transition from ferrimagnetic to ferromagnetic phase) in some mesoscopic magnets -Mn 12 Ac, Mn 6 Rad 6 and V 15 . These magnetic measurements provide us with a direct and unique method of determination of the exchange interactions between magnetic ions in magnetic moleculas. The knowledge of the magnetic interacion energies is important for molecular engineering in order to design new magnetic nanoscale materials with desireable properties. The intramolecule exchange integrals of the magnetic nanoclusters Mn 12 Ac, Mn 6 Rad 6 and V 15 that have been determined by this method are presented.