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Showing 10+ points and heart support (at least 3 cards). Remember that cuebids are forcing and so are unlimited. This cuebid should promise heart support and is forcing to 3. With a good hand and a suit, responder should just bid that suit.

Spades and a minor. This is called a "Michaels Cuebid" and is one of the more popular conventions. When they open a suit, and you (or partner) then cuebid that suit, it should show a hand with at least 5-5 distribution. It should have 5 cards in unbid majors so if a minor was opened, then shows both majors. Values for this bid depend on vulnerability and style.

Forcing; opener will typically bid 3NT with spades stopped. South could have a lot of different hands for 3 including good diamonds and very strong hearts. It's possible South has slam interest. That said, if South has one of those hands, South will bid again to clarify hand type. This is similar to asking what a takeout double means--yes, it could be a power double, but we never assume it is. We'll find out on South's next bid.

Promising a first or second round control of spades (with hearts as trump). Once you have a major suit agreed upon, you don't go hunting for notrump. Here, 3 shows a first or second round control (an ace, king, singleton or void). This should show interest in a heart slam.

Showing a singleton or void in diamonds, a game forcing hand, and 4+ hearts. This is a regular old splinter. Sometimes you don't want to overthink it. You're never looking for a stopper past the level of 3NT.

Natural, showing hearts and an opening hand. This is the one where you ignore the responder's suit. You would bid 2 naturally with something like:

 72  
AQJ1094 
A1072  
 3
 

Mixed raise in hearts. This is one that might be new to a lot of players. Typically jumping to 3 would be a weak raise, bidding 2 would be a strong raise, but what about a hand with 6-10 points and 4 hearts? You typically would have to bid 2 and then 3 later (giving your opponents time and space), but in modern bidding, this particular jump actually shows this hand. You don't have to adopt this, but it's a nice gadget if your brain has room for it.