Old English locian "use the eyes for seeing, gaze, look, behold, spy," from West Germanic *lokjan (cf. Old Saxon lokon "see, look, spy," Middle Dutch loeken "to look," Old High German luogen, German dialectal lugen "to look out"), of unknown origin, perhaps cognate with Breton lagud "eye." In Old English, usually with on; the use of at began 14c. Meaning "seek, search out" is c.1300; meaning "to have a certain appearance" is from c.1400. Of objects, "to face in a certain direction," late 14c.
Look after "take care of" is from late 14c., earlier "to seek" (c.1300), "to look toward" (c.1200). Look into "investigate" is from 1580s; look up "research in books or papers" is from 1690s. To look down upon in the figurative sense is from 1711; to look down one's nose is from 1921. To look forward "anticipate" is c.1600; meaning "anticipate with pleasure" is mid-19c. To not look back "make no pauses" is colloquial, first attested 1893. In look sharp (1711) sharp originally was an adverb, "sharply."
c.1200, "act or action of looking," from look (v.). Meaning "appearance of a person" is from late 14c. Expression if looks could kill ... attested by 1827 (if looks could bite is attested from 1747).