The eyepiece, also called the eyestick or similar names, was the part of the Dalek which enabled the Kaled mutant inside to see. Containing 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. (DW: Destiny of the Daleks)
The eyepiece was the most vulnerable part of the Dalek. When it was taken out or covered, the Dalek no longer remained a threat. After the eyepiece is destroyed, its head would spin around uncontrollably and the Dalek's weapon would be fired in a blind panic, usually accompanied by the frantic screaming of "My vision is impaired— I cannot see!"
However, post-Time War Daleks overcame this exploitable weakness. For example, a Dalek was shot in the eyestalk by Wilf with a paintball gun. The paint was immediately melted off and the Dalek was heard to say "My vision is not impaired." (DW: The Stolen Earth) After the Daleks harnessed background radiation as a power source during theLast Great Time War, they developed a shield for their casings that would melt bullets, making the eyepiece more protected and harder to take out. (DW: The Parting of the Ways)
To escape from the Dalek base, the Doctor threw his hat onto a Dalek's eyestick and the Dalek began firing and destroying the command center, almost hitting Davros in the process until the Doctor destroyed it. (DW: Destiny of the Daleks)
To escape from Davros' base in Tranquil Repose, the Doctor took out a Dalek's eyepiece and Peri attached a grenade to its casing, destroying the Dalek. (DW: Revelation of the Daleks)
During the Shoreditch Incident, Ace fired an ATR (Anti-Tank Rocket) at an Imperial Dalek and was shocked at the damage. She responded by saying "I aimed for the eyepiece." While inside a Dalek shuttle craft, the Doctor placed his hat on a Dalek's eyepiece to confuse it. (DW: Remembrance of the Daleks)
The viewpoint from the eyepiece varied over time, from a simple telescope-like view (DW: The Dalek Invasion of Earth) to an infrared scanner (DW: 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. (DW: 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. (DW: Dalek)
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. The viewpoint from this eyepiece is similar except for an opaque orange perimeter with honeycomb circuitry and protruding organic veins.