Magnetic field and angle dependences of the critical current density JcH, in epitaxial c-oriented YBa2Cu3O7−delta thin films are measured by the four-probe transport current technique, low-frequency ac magnetic susceptibility, and superconducting quantum interference device magnetometry. The films under study are deposited by off-axis dc magnetron sputtering onto r-cut sapphire substrates buffered with a CeO2 layer. A consistent model of vortex pining and supercurrent limitation is developed and discussed. Rows of growthinduced out-of-plane edge dislocations forming low-angle boundaries LAB’s are shown to play a key role in achievement of the highest critical current density Jc2106 A/cm2 at 77 K. The model takes into account the transparency of LAB’s for supercurrent as well as the pinning of vortex lattice on a network of LAB’s. Principal statistical parameters of the film defect structure, such as the domain size distribution and mean misorientation angle, are extracted from JcH curves measured in a magnetic field H applied parallel to the c axis and from x-ray diffraction data. An evolution of angle dependences Jc with H is shown to be consistent with the model supposing dominant pinning on edge dislocations. Strongly pinned vortices parallel to the c axis appear to exist in tilted low magnetic fields up to a characteristic threshold field, below which the magnetic induction within the film obeys a simple relation B=H cos . This feature is shown to explain the absence of the expected maximum of Jc at Hc in a low applied field. A peak of JcH and an angular hysteresis of Jc, which have been observed in an intermediate-field range, are discussed in terms of film thickness, surface quality, and orientation of the applied field. The observed effects are found to be consistent with the developed model.