An advanced twitter search screen is available, or use these operators from any search box:

General: Searches tweet text unless you toggle to people search.
Can toggle results between Top/All: Top is “most relevant” (don’t yet know how this is selected/ranked and behaves oddly if you click on Top multiple times), All is everything sorted newest to oldest (though if it isn’t everything, I’m not sure how I would know)
Search terms in tweet are in bold.

default operator is “and”
search in quotes for phrase search Punctuation is ignored within phrase.
OR for or operator, can use in lowercase to search for word “or”
-searchterm for NOT operator
#searchterm for tag search
from:username for tweets from that user
to:username for tweets to that user, only if username is first in tweet or only after RT and MT, not if listed later in tweet
@username for tweets mentioning that user
near:cityname searches for tweets from that city, does not work for countries/regions or cities within a larger region.
near:cityname within:distance limits by distance in mi or km
since:2010-12-27 for term since date in year-month-day format
until:2010-12-27 for term until date in year-month-day
searchterm :) Twitter says “for term with positive attitude” but looks like this is a search for :) :-) or :P (search for :-) and :P also work the same)
searchterm :( Twitter says “for term with negative attitude” but looks like this is a search for :( :-( (interchangeable in search, same as above)
? for question mark in tweet (other lone punctuation seems to be ignored)
filter:links for tweet with URL
filter:images for tweet with images (not yet listed?)
filter:videos for tweet with videos (not yet listed?)
source:twitterfeed (or any other posting method) to search by posting method
lang:en for tweets in English, lang:fr in French, etc.