Look Up, Look Down

As a phrasal verb, to look up means the future seems positive. The full expression, "Things are looking up.", means the future seems generally positive for the person. This expression is the most common, by far.

Look up has the added meaning of researching a piece of information, usually in a directory. Example: #1) I looked up his phone number in the phone book. #2) I looked up the word in the dictionary. #3) I've never heard of Harry Partch, but I will look him up on Wikipedia tonight.

Look down may have the opposite meaning of the phrasal verb look up (i.e. Things are looking down.) However, there is a more common expression, "Things aren't looking good", which means the future of a situation seems negative.

Look down has the added meaning of feeling/expressing contempt for someone, or not having respect for someone. Example: #1) He looks down on poor people because he believes they're lazy. #2) My brother looks down on me because of my drug addiction. #3) My wife looks down on me because I cannot last for more than three minutes in bed.