The Vatican is the smallest sovereign state in the world and functions in practice as a set of destinations inside Rome: St Peter's Basilica and its square, the Vatican Museums ending at the Sistine Chapel, and the gardens accessible only on guided visits. There is no border control — you walk in from the Roman street grid.
The guides here cover the Vatican as a whole. Queues are the defining practical issue: museum entry runs on timed tickets that sell out, and the basilica has a separate security line that is longest in the middle of the day. A dress code covering shoulders and knees is enforced at both, and papal audiences on Wednesdays change access patterns across the whole area.