A drilling apparatus (1) provides continuous rotation, and in some embodiments also vertical translation of the drill bit, such that weight can be kept on the bit and drilling can continue uninterrupted during connections. The connection is made in a pressure chamber formed by seals (2, 4) and spacers (15, 16). An upper snubber (5) grips the drill string above the joint and a lower snubber (6) grips it below the joint. The top drive is decoupled as the snubbers take over drill string drive, and apply a differential torque so that the connection is made. This achieves continuous rotation during the connection, and by use of an extension sub (18) drilling is also continuous.