3D glasses

3D glasses were a facial accessory which could enhance 3D effects. (TV: The Doctor Appears)

The Doctor
The Doctor, at least in their tenth incarnation, used 3D glasses on at least two occasions. (TV: Army of Ghosts, Doomsday) He used them to examine the Sphere before identifying it as a Void Ship, a hypothetical craft for travelling through the nothingness between parallel universes. (TV: Army of Ghosts)

Others
During a live performance, Dermot O'Leary had Claudia Winkleman wear a pair of 3D glasses to watch an exclusive clip of a "special 3D episode of Doctor Who", (TV: The Doctor Appears) known as The Day of the Doctor, (WC: The Zygon Isolation) and experience the Doctor "as [she'd] never seen him before". After she put on the glasses and the clip began, the actual Eleventh Doctor appeared on stage, "in 3D". Winkleman then began touching the Doctor, noting that it was "like 3D [she'd] never experienced-", and noted that she could "even smell him!", before Dermot instructed her to take the glasses off, after which she realised it was actually the Doctor, rather than a 3D illusion, which she noted as "awkward". This resulted in the Doctor stating that he "[wouldn't] be sniffed", and keeping his distance from her. (TV: The Doctor Appears)

Minor references
Gino Gonzalez once wore a T-shirt with a depiction of 3D glasses on it. (COMIC: Revolutions of Terror)

Information from invalid sources
The Eleventh Doctor once called to an unseen audience to "activate [their] 3D spectacles". (NOTVALID: Cinema Introduction to The Day of the Doctor)

Other matters
As stated in TV: The Doctor Appears, The Day of the Doctor was an episode of Doctor Who which was screened in 3D in theatres.