When is an aircraft cleared to land? In Is there a minimum separation between a landing aircraft and another crossing its runway? it was explained that once an aircraft has clearance to land, that runway is reserved for the exclusive use of that aircraft.

At busy airports you can usually see a long line of four or more airliners descending a glideslope towards a runway.


Image by nustyR AirTeamImages (found via LondonReconnections)

Looking at FlightRadar24, the time between aircraft appears to be of the order of about 85 seconds according to my stopwatch.



It seems as if, by the time the previous aircraft has turned off the runway, the following aircraft has a very short time to obtain clearance or decide to go around.

At what point is each aircraft given clearance to land by ATC?
Usually, the clearance is given when the runway is clear of traffic or, at least in Europe, when two conditions are met:


Reduced Runway Separations is in use and the criteria for issuing the landing clearance are met.
The previous traffic will have left the runway when the following aircraft crosses the threshold. (Non-withheld landing clearance)



  321.5 Landing clearance need not be withheld until prescribed separation exists 
  if there is reasonable assurance that the appropriate separation will exist 
  when the aircraft crosses the runway threshold. However, do not clear an 
  aircraft to land before a preceding landing aircraft has crossed the runway 
  threshold.


Aircraft can also be made aware to expect a late landing clearance.

Clearing multiple aircraft to land in a sequence on the localizer is not used in countries operating under ICAO rules. This is more of an FAA procedure, as described in the other answers.