A machine tool is provided with a vertically aligned tool spindle, which is equipped for accommodating tools and which is movable in a vertical direction and in a first horizontal direction. The machine tool further comprises at least one jig for clamping workpieces to be machined. The at least one jig is movable in a second horizontal direction. The tool spindle and the at least one jig are arranged on a common machine frame. There is also provided a workpiece transport device, which is arranged on the machine frame, and which is adapted to perform at least one of introducing unmachined workpieces into the at least one jig and removing machined workpieces from the at least one jig. There is also provided a corresponding method of machining workpieces.