The sonic sunglasses were a device the Twelfth Doctor used to replace his sonic screwdriver after he abandoned it. They were worn as normal, black sunglasses with no visible difference to normal sunglasses.
He wore them during his three week visit to Essex in 1138. He referred to them as "wearable technology". (TV: The Magician's Apprentice) He used them to recall the TARDIS after it had been dispersed by the HADS "dispersal" function. He expressed concern that, whilst in the possession of Davros, they might have become scratched. (TV: The Witch's Familiar)
The Doctor used them again in the underwater base the Drum in the year 2119 to connect to the base's Wi-Fi to allow the base crew to view the trapped ghosts from his position. He also appeared to use them to scan the markings on the wall in an alien spaceship. (TV: Under the Lake) He later used them to project a hologram of his likeness as one of the ghosts and to erase the markings from everyone's minds. (TV: Before the Flood)
The Doctor attempted to use them to scare a group of Vikings, only for their leader to snap them in half. Clara later recovered half of them and used it to trick the Mire into believing her to be a threat to avoid, but failed to prevent a conflict when Ashildr declared war against them. After defeating the Mire, the Doctor reclaimed the broken half of the glasses kept by Odin and was able to hack their teleporter to send him back to their ship, and also reprogram a Mire repair kit to save Ashildr from death. (TV: The Girl Who Died)
The Doctor later either repaired or replaced the sonic sunglasses. He used them to light a candle in 1651 England. (TV: The Woman Who Lived) He used them to unlock Osgood's chains in the early 21st century. (TV: The Zygon Invasion) After Osgood's glasses broke in half, the Doctor lent her his sonic sunglasses for a while. She used them to break into a van, using setting 137. The Doctor used them to trigger the memory wiping devices in the Black Archive. They apparently had a browsing history, which the Doctor advised Osgood not to view. (TV: The Zygon Inversion)
When the Doctor was trapped in his confession dial (TV: Heaven Sent) over the span of four and a half billion years, (TV: Hell Bent) he used the sonic sunglasses to examine a crystalline structure blocking the exit home only to discover it was Azbantium. He then put them on when returning to Gallifrey and proclaimed "the Hybrid is me". (TV: Heaven Sent)
Clara later used them to spy on the Doctor and Me talking about the Hybrid at the end of time. Afterwards she used them on the neural block the Doctor stole from the Time Lords to reverse the settings to cause it to erase his own memory. Before losing his memory of her, Clara tucked the sunglasses into the lining of the Doctor's jacket. Later, while searching for Clara by reconstructing the gaps in his memory, the Doctor used the sonic sunglasses to connect his guitar to a radio, making it act like an amplifier.
The sonic sunglasses left the Doctor's possession unbeknownst to him after Me and Clara's TARDIS diner dematerialised, taking them with it. The TARDIS later gifted the Doctor with a new sonic screwdriver. (TV: Hell Bent) He later got another set of sunglasses which he employed alongside his new sonic screwdriver. He used them to examine a hologram projection of the Halassi Androvar diamond embedded in King Hydroflax' head. (TV: The Husbands of River Song)
When Skinks attempted to throw the Doctor and Heddy Garber into their ship's black hole drive, the Doctor used the sunglasses to deactivate the containment field around the black hole. (COMIC: Pirates of Vourakis)
He later wore them after being rendered blind due to being exposed to the vacuum of space. (TV: Oxygen) While blind, the Doctor adapted the sunglasses so that they would upload information directly to his brain, allowing him to maintain at least some degree of independence and hide the fact that he couldn't see. When an alien race created an illusion of Earth to prepare for their invasion, the illusion of the Doctor was so sophisticated that he was able to email everything he had experienced for the last few hours of the illusion directly to the real sonic sunglasses to warn his real self about the planned invasion. (TV: Extremis).
The real Doctor later used the sonic sunglasses to guide him as he dealt with the Monks and their plot to get the world leaders to consent to their rule of the Earth by promising to stop a world-ending event in exchange. The sonic sunglasses enabled the Doctor to continue to hide his blindness and function independently. He was also able to use them as a cell phone, communicating with people through their cell phones by holding his finger to the side of the sunglasses. He was also able to use the sonic sunglasses to put all the classified information on labs on the UNIT watchlist onto the Internet in a searchable format. However, the sonic sunglasses were not perfect in replacing the Doctor's eyes and could not display the numbers on a combination lock for the Doctor to escape an explosion he had set. Bill was forced to make a deal with the Monks to save the Doctor as a result. (TV: The Pyramid at the End of the World)