The standard interpretation of the phase diagram of type-II superconductors was developed in the 1960s and has since been considered a well-established part of classical superconductivity. However, upon closer examination a number of fundamental issues arises that leads one to question this standard picture. To address these issues we studied equilibrium properties of niobium samples near and above the upper critical field H_c2 in parallel and perpendicular magnetic fields. The samples investigated were very high quality films and single-crystal disks with the Ginzburg-Landau parameters 0.8 and 1.3, respectively. A range of complementary measurements has been performed, which include dc magnetometry, electrical transport, muon spin rotation spectroscopy, and scanning Hall-probe microscopy. Contrary to the standard scenario, we observed that a superconducting phase is present in the sample bulk above H_c2 and the field H_c3 is the same in both parallel and perpendicular fields. Our findings suggest that above H_c2 the superconducting phase forms filaments parallel to the field regardless of the field orientation. Near H_c2 the filaments preserve the hexagonal structure of the preceding vortex lattice of the mixed state, and the filament density continuously falls to zero at H_c3. Our paper has important implications for the correct interpretation of the properties of type-II superconductors and can be essential for practical applications of these materials.