Most modern vehicles have independent suspensions on the front wheels.
Many vehicles also have An independent rear suspension (IRS), as the name implies, has the rear wheels independently sprung. A fully independent suspension has an independent suspension on all wheels.
Independent suspension typically offers better ride quality and handling characteristics, due to lower 'unsprung weight' and the ability of each wheel to address the road undisturbed by activities of the other wheel on the vehicle.
Independent suspension requires additional engineering effort and expense in development versus a live axle or beam axle arrangement. A very complex IRS solution can also result in higher manufacturing costs.
The key reason for lower 'unsprung weight' relative to a live axle design is that, for driven wheels, the differential unit does not form part of the unsprung elements of the suspension system. Instead it is either bolted directly to the vehicle's chassis, or more commonly to a subframe.
The relative movement between the wheels and the differential is achieved through the use of swinging driveshafts connected via universal (U) joints, analogous to the constant-velocity (CV) joints used in front wheel drive vehicles.