An intrinsic part of any exclusion zone is going to be checkpoints. Without them unsuspecting, and in some cases unscrupulous, people would gain unrestricted access to a still potentially toxic and dangerous environment. At the moment there are eleven that I could find, as per the location pins on the map below.
Almost all visitors to the exclusion zone will go via the checkpoint at Dytiatky - one of the most photographed checkpoints on the planet.
Dytiatky Checkpoint - The way in and out for almost all visitors to the zone
Within the zone, such at Pripyat, the checkpoints are less elaborate, with often just one man and a barrier. However, to have got this far you would have first needed to pass the more official checkpoints where all paperwork would have been validated before you went any further.