notfrequentenough Welcome to the forum ^
There are 3 main airline alliances.
http://www.oneworld.com/
http://www.staralliance.com/en/
http://www.skyteam.com/
As PP's comment above with these alliance's you can (but not always) earn miles in your frequent flyer program [FFP] by flying another airline in you alliance. It does depend on the ticket. For example you can get Qantas miles (points) for BA flights.
You cannot combine miles or transfer between airline program's. In general once in an airline FFP that's where they stay.
Upgrade are a good use of miles for many. Apart from some minor exceptions, upgrades with an airline miles/points can only be on a segment that is both marketed (airline flight number) and operated by the airline (metal). But not all tickets are eligible to upgrade with FFP miles/points
Be aware that in most freq flyer program miles expire if no activity, Typically after 18 months, 1 years or 2 years:- depends on the program