FeSe is structurally the simplest iron-based superconductor but one of the most intriguing electronically, with extreme tunability in its electronic and superconducting properties. With a superconducting transition of Tc~9K, FeSe undergoes a structural transition at Ts~87K but does not order magnetically at any temperature. Furthermore, it shows a strong increase in its superconductivity from 8.7K to 37K under pressure, which occurs in the presence of a new unknown magnetic phase. Our proposal is to understand the origin of the enhanced superconducting phase of FeSe by investigating the origin of the structural and magnetic phase in high quality single crystals of FeSe under pressure.