A drilling system for drilling a lateral borehole from a main borehole comprises a tubular conduit through which a fluid can be pumped, and a drilling assembly connected to the tubular conduit so as to receive fluid pumped therethrough. The drilling assembly comprises a power conversion unit, through which the fluid flows and which operates to provide a downhole power output; a drilling unit including a drilling apparatus powered by the output of the power conversion unit and operable to drill a lateral borehole into the formation surrounding the main borehole, and a liner unit for storing one or more liners for installation into the lateral borehole; and an anchor unit operable to anchor the drilling assembly in the main borehole when the drilling unit operates to drill the lateral borehole. A method of drilling a lateral borehole from a main borehole using such a drilling system comprises positioning the drilling assembly in the main borehole at a location of interest using the tubular conveyance; anchoring the drilling assembly in the main borehole using the anchor unit; operating the drilling unit to drill a lateral borehole from the main borehole; retrieving the drilling unit from the lateral borehole; releasing the anchor unit; and moving the drilling assembly to another location.