The pressure evolution of RbBH(4) has been characterized by synchrotron powder X-ray diffraction and Raman spectroscopy up to 23 GPa. Diffraction experiments at ambient temperature reveal three phase transitions, at 3.0, 10.4, and 18 GPa (at 2.6, 7.8, and approximately 20 GPa from Raman data), at which the space group symmetry changes in the order Fm-3m(Z=4) --> P4/nmm(2) --> C222(2) --> I-42m(4). Crystal structures and equations of state are reported for all four phases. The three high-pressure structure types are new in the crystal chemistry of borohydrides. RbBH(4) polymorphs reveal high coordination numbers (CNs) for cation and anion sites, increasing with pressure from 6 to 8, via an intermediate 4 + 4 coordination. Different arrangements of the tetrahedral BH(4) group in the Rb environment define the crystal symmetries of the RbBH(4) polymorphs. The structural evolution in the MBH(4) series is determined by the cation's size, as it differs drastically for M = Li (CNs = 4, 6), Na (CN = 6), and Rb. The only structure common to the whole MBH(4) family is the cubic one. Its bulk modulus linearly decreases as the ionic radius of M increases, indicating that the compressibility of the material is mainly determined by the repulsive BH(4)...BH(4) interactions.