The newer systems still use inertial as primary. As autoflight stated the newer inertial navigational system will position update via GPS, as well as DME inputs, when available. This corrects for position error throughout the flight.
The IRS will also continually monitor its position error rate (which should not be more than around 1-2 nm per hour) and on landing calculate a summed error rate over the flight and correct itself to counter this error rate. This happens on a continual basis and will take into account the wear rate of all components in the system, to allow a 'component lifetime' of accurate use within error rate limits.
The older INS system (obsolete now except for older models still in operation) utilized a gimbal stabilized platform to navigate. The latest IRS units are laser ring gyro's (strapdown) and the very latest utilize fibre optic cable in place of the laser ring system for even greater accuracy, which I believe can be as low as 0.5 nm per hour which is a perfectly acceptable position error rate in any accurate navigation system.
I am not sure if GPS will take over as the primary navigation reference system as it is dependent on signals external to the aircraft for reference. The inertial systems are entirely self contained and extremely accurate.