The intercalation of hydrogen into the layered structure of MoO3 produces four hydrogen molybdenum bronze phases H(x)MoO3 (0 < x < 2). The correlation between the structure and the physical properties of these low-dimensional conductors has been investigated by X-ray diffraction and conductivity measurements. Powder diffraction studies revealed phase transitions as a function of temperature and hydrogen content. A new proton-distribution model describes the lattice distortions resulting from the intercalation in the whole composition range. Superstructure reflections were detected in precession photographs of single crystals of the phases I (x = 0.3) and III (x = 1.6). A single-crystal structure determination was performed for H0.33MoO3, which exhibits a 3a x 6c superstructure at ambient temperature. Structural and experimental data for this particular composition are: P21/b 11, a = 11.70 (1), b = 14.070 (5), c = 22.40 (2) angstrom, a = 90.0 (1)-degrees, V = 3687 (8) angstrom, Z = 72, D(x) = 4.68 (1) Mg m-3, lambda(Mo Kalpha) = 0.7107 angstrom, mu = 0.593 cm-1, F(000) = 4622.6, R(F) = 0.10 for 1223 unique reflections. Valence-sum calculations revealed that all the protons of H0.33MoO3 are located in periodically arranged 6-(OH)-clusters. The long-range proton ordering breaks down at T(c) = 380 K giving rise to a second-order phase transition. The identification of this transition as a Peierls distortion explains many properties of phase 1: conductivity measurements show a metal to non-metal transition at T(c) with an unusual temperature dependence of sigma in the ordered phase. The multiplication of the unit cell along the c direction as well as T(c) depend on the hydrogen content x. The critical exponent of the order parameter beta = 0.36 is compatible with an incommensurate superstructure. Frohlich conductivity as a result of charge-density-wave depinning is observed in field-dependent conductivity measurements.