ITA Matrix is the main database upon which flight search engines are built... and you can use advanced codes to unlock features you otherwise would miss on Kayak, Google Flights or other searche engines to get the best deal. Finding the best fare can really stretch the value of your points.
#1: Nearby Radius
Aggregate all airports within 25-2000 miles of your destination... airports you didn't know existed. This can be especially helpful for "positioning flights", when you just want to get to a far region of the world (Hong Kong, Munich, etc.) and then take a local budget carrier.
#2: Full Calendar of Lowest Fares
Plot 30-day calendar (which can include variable duration and lots of airport combinations). Search # of nights in your destination with up to week difference (5-12, 13-20, etc.)
#3: Include a Stopover
This is my favorite hack, two trips for the price of one! Program a stopover greater than 24-hours (1,440 minutes) using "X" and "minconnect 1440". If you want a specific connection airport, use its IATA code instead of "X".
#4: Exclude Specific Airlines
Filter out airlines with the exclusion symbol ("~") the airline code and a "+" sign. For example, if you dislike Spirit airlines, filter them out using ~NK+.
#5: Compare 1-Ways for "Hacker Fares"
To fly there on one airline and back on another requires searching two one-way searches, as round-trip will stick with a specific airline.
Appendix of Codes for Advanced Users
"Nearby" allows multiple city-to-city combos within X mile radius
30-day calendar of lowest fares w/ variable length of stay of up to 7 days difference (i.e. 5-12 days or 13-20)
Duration: Sort or slide a filter by overall length of itinerary to return shortest trips or longest stop-overs.
"~" means "exclude"
example: ~NK (excludes Spirit Airlines, shows ONLY direct flights)
example: ~NK+ (excludes Spirit Airlines, allows options with connections)
example: ~ORD (excludes any connections in Chicago O'Hare)
"X": Connection (i.e. any connection, no city specified)
example: X / minconnect 1440 (24-hour stopover)
"+" 1 or more (allows connections)
AA (just returns direct flights on American)
AA+ (includes flights with connections on American)
"?": 1 OR 0
"X?" is 1 stop or direct
"ATL?" is direct or a stop in Atlanta
"FLL?" is direct or a stop in FLL
"Airport Code": Connection city
example: "ATL, FLL" (connects in either of these airports, not both)
"F": flight (think of this as a placeholder)
"F F F" means 3 flights
"F? b6" means one flight (direct or more) and then Jet Blue
"F+ b6+" allows for connections
"F? ATL F? / minconnect 720" is one flight, 720 minutes in Atlanta, then one flight
"/ minconnect [# of minutes]" how long a connection you require
"/ -airlines NK"
"/ padconnect [# of minutes]" adds time to the min connection