The Doctor is getting used to being blind with the use of sonic sunglasses, well, it did seem logical after the sonic screwdriver didn't it. The Doctor is in a lecture hall when Nardole arrives to announce that the Pope has arrived to see him.
The Pope wants the Doctor's help in solving a puzzle where when people read the Veritas, the person commits suicide. The Doctor along with Nardole and Bill Potts are taken to the secret vaults of the Extremis under the Vatican in Vatican City.
Nardole and Bill Potts are sent to explore the Extremis whilst the Doctor reads from the Veritas to understand what is going on. Nardole and Bill Pott eventually find that they are in a giant machine which allows them access to different places in the world including CERN, the headquarters of the European Centre for Nuclear Research. It later turns out the whole set up is an elaborate computer simulation by a group of aliens who plan to take over the Earth. The aliens built the simulation to work out how the Earth and the Doctor would respond to the invasion.
Also in the episode is a flashback of the Doctor on an alien world who is overseeing the execution of another timelord. The Timelord in question turns out to be Missy. Instead of killing Missy, the Doctor in effect rescues Missing promising to put her in a safe place. It turns out the big secret running through the series was that Missy was in the vault at the University.
There does seem to be influences from Dan Brown's 'Angels & Demons' which features both CERN and the Vatican.