"What exactly is meant when one is cleared for the visual approach to runway xx? Is the pilot on his own to descend and land as if VFR? Any requirements beyond this?"- Mike R.
“The AIM defines Visual Approach as an approach conducted on an instrument flight rules (IFR) flight plan which authorizes the pilot to proceed visually and clear of clouds to the airport.
The pilot must, at all times, have either the airport or the preceding aircraft in sight. This approach must be authorized and under the control of the appropriate air traffic control facility.
The reported weather at the airport must be ceiling at or above 1,000 feet and visibility of 3 miles or greater. A visual approach clearance does not authorize you to enter clouds again.
An important point to remember is that there is no missed approach procedure for a Visual Approach. If you lose sight of the airport or have to go around for some reason, a new clearance is required.”