Very detailed magnetic irreversibility data for fields applied along the c axis or the ab plane of a pure and untwinned YBa 2 Cu 3 O 7Ϫ␦ single crystal and Sr-doped and heavily twinned YBa 2Ϫx Sr x Cu 3 O 7Ϫ␦ (xϭ0.25, 0.37, and 0.5͒ single crystals are reported. The irreversibility lines T irr (H) of the pure single crystal show a considerable planar anisotropy but follow the same power-law regime, for both field orientations, arising within the conventional flux-creep theories in the whole field range. Very differently, however, the T irr (H) lines of the doped superconductors exhibit besides large anisotropies, several different regimes. In fields lower than 8 kOe the T irr (H) data of the doped samples display the de Almeida-Thouless ͑AT͒ and Gabay-Toulouse ͑GT͒-like power-law behaviors, the signature of a frustrated superconductor. For higher-field values, and in particular for Hʈc, flux dynamics seems to be conventional. However, for Hʈab and field values above 30 kOe, the flux dynamics displays sharp directional properties along the twinning planes ͑TP's͒ for rotations about the c axis. This behavior is cusplike, comparable to that caused by columnar defects, which characterizes a Bose-flux-glass phase. We appoint the superconducting granularity and frustration as responsible for the AT and GT behaviors below 8 kOe and the strong anisotropic pinning for H parallel to the TP's as the cause of the Bose-glass features. On the other hand, the isotropic pinning for large angular displacements or for any angle in fields below 30 kOe is the most probable cause of the vortex-glass features.