How invisibility (and stealth in general) is handled in 4e….
First off, there's two different types of being invisible- invisible while hidden, and invisible while not hidden.
Let's say someone is in the middle of combat, and does something that makes them invisible. Unless they begin making Stealth checks, they're not hidden- only invisible. In other words, someone who is invisible, but doesn't make a stealth check (or they make a check and are beaten) can still be targeted as normal. Anyone who wants to can know exactly what square they're in, no matter what. They still have total concealment, so attackers take a -5 on attack rolls with melee and ranged attacks (area attacks, such as breath weapons or close bursts, take no such penalty against foes that are invisible but not hidden), and they still gain combat advantage, but unless they make a stealth check every round and succeed, the players can all know where they are.
If they DO make the stealth checks, though, they're invisible (i.e., the DM can just pull the mini off the board and have them pop back up whenever they would become visible). But, again, only if they make their stealth checks.
Oh, and also, attacking only makes you become visible if the power that made you invisible says so. So if something makes you invisible until the end of your next turn, no matter what you do, you're invisible until the end of your next turn. (The Ring of Invisibility, for example, makes you invisible until you're hit by a melee or ranged attack.)
Most of this (particularly the invisible but not hidden bit) is from some fairly recent errata. But, just to recap, if you don't make a stealth check, you can still be targeted as normal while invisible, area attacks suffer no attack penalties against invisible foes, and you only become visible when the power says you become visible.