In this dissertation, we present a theoretical study of compounds rich in hydrogen, focusing on their crystal structure and potential metallization as pressure is applied. Chapter 1 is an introduction to metallic hydrogen; it reviews previous studies and suggests a new way of analyzing the geometric changes that ensue as pressure is applied. Chapter 2 describes the search for structures for SnH4 , using chemical intuition and random search algorithms. Chapter 3 deals with the general problem of segregation which arises as SnH4 , a thermodynamically metastable (positive heat of formation from Sn and 2H2 ) but kinetically persistent compound, is compressed. Chapter 3 is a complement to Chapter 2, as layered structures arise naturally in the low pressure regime, prompting us to explore the subject. Chapter 4 begins an ambitious project which strives to understand the electronic structure and properties of metallic hydrides of the form MH x , where M= Si, Sn and W, and x = 4, 6, 8, 10, 12. For n > 4, there exist van der Waals complexes at lower pressures, but show great variation in structure as they metallize at higher pressures. Chapter 5 explores the effect of impurities in the DOS, as swapping of atoms in structures of stoichiometry Liy[-]1 Bey H. The parent LiBe phase is stable at high pressures; here we attempt to lower the pressure for its metallization by H substitution