Dalek eyestalk

The Dalek eyestalk, also called the eyepiece, eye antenna (COMIC: The Trodos Ambush) tele-eye, (COMIC: The Daleks Are Foiled) or eye-stick (PROSE: Mission to the Unknown) was the part of the Dalek which enabled the Kaled mutant inside its shell to see outside of its shell.

The Special Weapons Dalek notably had neither an eyepiece nor luminosity dischargers. (TV: Remembrance of the Daleks)

Design
The Dalek eyestalk was mounted on the Dalek's dome and enabled the Dalek to see its surroundings. It was the only vulnerable part of the Dalek. (TV: Resurrection of the Daleks)

The Daleks produced by the Progenitor had radically redesigned eyepieces with black rings on the stick, fins on the cone, and the lens being organic rather than robotic, much like a real organic eye. The viewpoint from this eyepiece was similar, except for an opaque orange perimeter with honeycomb circuitry and protruding organic veins. (TV: Victory of the Daleks)

Abilities
With a wide-angle lens, the eyepiece could magnify images so that the Dalek could see across great distances and also track a person's footsteps. (TV: Destiny of the Daleks) The eyepiece was the most vulnerable part of the Dalek. Dalek eyestalks from a post-Last Great Time War era were capable of even greater forms of magnification, with various scales displayed in-vision.

The viewpoint from the eyepiece varied over time, from a simple telescope-like view (TV: The Dalek Invasion of Earth) to an infrared scanner (TV: Destiny of the Daleks) to a bright green (or white, in the case of Imperial Daleks) lens, with Kaled script readouts displayed in the top and bottom left corners with target cross hairs allowing the Dalek to line up its targets. (TV: Remembrance of the Daleks) By the time of the Last Great Time War, the eyestalks all contained blue glowing lenses, with a targeting aid "on-screen" at all times, and a magnification ability - one Dalek used this mode to zoom in on Rose Tyler's face. (TV: Dalek) Eventually, the viewpoint was once again redesigned into a slightly green-tinted appearance. This variant was capable of administering x-ray scans, with one being performed by one Dalek in order to confirm the existence of the Doctor's binary vascular system. (TV: Resolution)

Weaknesses
If the eyepiece was destroyed or if the lens was covered, the now-blind Dalek became a reduced threat. Daleks would behave erratically under these circumstances as the creature inside the casing was unable to deal with any danger because it was unable to see them. They would move around uncontrollably and fire their weapons in a blind panic, usually accompanied by the frantic screaming of "My vision is impaired! I cannot see!". (TV: The Daleks, The Daleks' Master Plan, Resurrection of the Daleks, Revelation of the Daleks, Remembrance of the Daleks, The Parting of the Ways)

Whilst on Skaro, in order to escape from the Dalek base, the Fourth Doctor threw his hat onto a Dalek's eyestalk. The Dalek began firing incandescently in a panic, guided by Davros though it had trouble obeying the orders because it was too panicked to concentrate on the Doctor, and almost hitting Davros in the process until the Doctor destroyed it. (TV: Destiny of the Daleks) The Second Doctor previously used the same tactic against Dalek 4 on Trodos, allowing him to penetrate its inner hearing system with his recorder and render it berserk. (COMIC: The Trodos Ambush)

During the Shoreditch Incident, Ace fired an ATR (Anti-tank rocket) at an Imperial Dalek's eyestalk. The ATR destroyed the top half of the Dalek, and the Seventh Doctor was shocked at the damage. Ace responded by saying "I aimed for the eyepiece". She later used a baseball bat enhanced by the Hand of Omega to sever a Dalek's eyepiece. While inside a Dalek shuttle craft, the Doctor merely placed his hat on a Dalek's eyepiece to confuse it while he "shorted it out". (TV: Remembrance of the Daleks)

However, post-Last Great Time War Daleks mostly overcame this exploitable weakness. Their shielding could resist most bullets, although bastic bullets were still somewhat effective in blinding a Dalek. (TV: The Parting of the Ways) They could also melt any hindrance, as Wilfred Mott discovered when he shot a Dalek eyestalk with a paintball gun. The paint was immediately melted off after a moment and the Dalek was heard to say "My vision is not impaired". (TV: The Stolen Earth)

The Daleks of the New Dalek Paradigm had the ability to repair their vision if their eyestalk was damaged, so the weakness could only be exploited as a temporary distraction. (TV: The Big Bang, GAME: The Eternity Clock) However, repairs could not be made if the eyestalk was severed from the main casing or if the damage was too great. (COMIC: The Only Good Dalek, The Dalek Project)

Other uses
Dalek eyestalks were worth a considerable amount during the Second Dalek War of the 26th century. They were collected by Dalek Killers and bounty hunters and were worth 20 decacredits after they were returned to the Earth forces to confirm a kill. Some people like Jon Bowman and his crew on-board the Wayfarer did this for a living. (PROSE: Love and War, Prisoner of the Daleks) Outside of times of war, eyestalks still had value and could attest to someone's character since killing a Dalek was no small feat. The Doctor in his eleventh incarnation once salvaged the eyestalk of a damaged Supreme Dalek to use as bartering leverage with Gantok to learn more about the Silence. (TV: The Wedding of River Song) On another occasion, the Doctor used an eyestalk to display proof of his courage and comradeship to gain the trust of one of the many fleets besieging Trenzalore, before realising he had landed on a Dalek ship who immediately attacked him. (TV: The Time of the Doctor) He kept the eyestalk of a Dalek from the Time War in the TARDIS drawing room. (GAME: TARDIS, The Gunpowder Plot)

A Dalek Supreme sent to 26th century Spiridon had the unusual feature of a lamp in its eyestalk lens. It held the same communications function as a regular Dalek's luminosity dischargers on the sides of its head, lighting up when it spoke. (TV: Planet of the Daleks) Another Dalek, the immediate subordinate to the Emperor that was part of the mission on Kar-Charrat to obtain information, had the same eyestalk like the member of the Supreme Council. (AUDIO: The Genocide Machine)

While on Skaro, the Eleventh Doctor sent Amy Pond to salvage a Dalek eyestalk, which he needed to create the Dalek Vision Disruptor to blind the rest of the Daleks. (GAME: City of the Daleks)

The Daleks' humanoid puppets also had eyestalks, which emerged from their foreheads. (TV: Asylum of the Daleks, PROSE: The Dalek Generation, TV: The Time of the Doctor, TV: The Magician's Apprentice)

The robotic Dalek that the Doctor dubbed Quasimodo Dalek had two eyestalks, both in place of its gunstick and manipulator arm. A gunstick was attached where the eyestalk should have been. (COMIC: The Dalek Project)

Rusty's eyestalk was used by the Twelfth Doctor, Clara, and a team from the Combined Galactic Resistance as an entry into the Dalek once they were miniaturised in order to undertake their mission to uncover why the Dalek became good. (TV: Into the Dalek)