A drilling rig adapted to perform drilling and/or other wellbore related activities, the drilling rig comprising: - a drilling tower, - a drill floor with a well center positionable above a wellbore, - a slip device arranged at the well center and adapted to suspend a drilling tubulars string in the wellbore, - a tubulars connection makeup and breaking device near the well center, - a top drive system, - a vertical motion drive (211,212,215,216,217,218) adapted to cause vertical motion of the top drive system relative to the drilling tower in order to perform drilling and tripping operations, - a fingerboard device (71,72) adapted to store drilling tubulars stands, wherein the drilling tower is provided with one or more vertical rails (17,18) parallel to a vertical firing line that extends through the well center, wherein the top drive system comprises: - a traveling carriage that is vertically mobile along said one or more vertical rails of the drilling tower by means of said vertical motion drive, - a top drive unit supported by said traveling carriage and comprising a top drive motor and a rotary torque output member, e.g. a rotary stem, adapted to be engaged with a top end of a drilling tubulars string extending in a firing line through the well center to impart torque to said drilling tubulars string in order to perform drilling operations, wherein the top drive system further comprises a tripping operation elevator that is adapted to be engaged with a drilling tubulars string or drilling tubulars stand, e.g. with the top end thereof, in order to perform tripping operations, characterized in that the top drive unit and the tripping operation elevator are each mobile relative to the traveling carriage, and wherein the top drive system is provided with one or more actuators adapted to cause said relative motion of the top drive unit and of the tripping operation elevator so as to provide: - a drilling mode, and - a tripping mode, wherein, in said drilling mode, the top drive unit is in operative position with the rotary torque output member being aligned with the firing line and wherein the tripping operation elevator is in a non-operative position remote from said firing line, and wherein, in said tripping mode, the tripping operation elevator is in operative position being aligned with the firing line and wherein the top drive unit is in a non-operative position, and wherein the top drive system is embodied such that, in said tripping mode, an unobstructed zone is present vertically above the tripping operation elevator allowing the top drive system to be lowered along a drilling tubulars stand in the firing line above the well center, at least so that the top drive system is below the top end thereof, e.g. allowing lowering till near the well center on the drill floor, whilst the drilling tubulars stand is disconnected by means of the tubulars connection makeup and breaking device, and wherein the top drive system is embodied such that, in said tripping mode and with the top drive system lowered at least below the top end of said drilling tubulars stand, said drilling tubulars stand is removable from the firing line, primarily in lateral direction, to allow for placement of said drilling tubulars stand in said fingerboard device (71,72). - a drilling tower, - a drill floor with a well center positionable above a wellbore, - a slip device arranged at the well center and adapted to suspend a drilling tubulars string in the wellbore, - a tubulars connection makeup and breaking device near the well center, - a top drive system, - a vertical motion drive (211,212,215,216,217,218) adapted to cause vertical motion of the top drive system relative to the drilling tower in order to perform drilling and tripping operations, - a fingerboard device (71,72) adapted to store drilling tubulars stands, - a traveling carriage that is vertically mobile along said one or more vertical rails of the drilling tower by means of said vertical motion drive, - a top drive unit supported by said traveling carriage and comprising a top drive motor and a rotary torque output member, e.g. a rotary stem, adapted to be engaged with a top end of a drilling tubulars string extending in a firing line through the well center to impart torque to said drilling tubulars string in order to perform drilling operations, - a drilling mode, and - a tripping mode,