Invisible attacking creatures get a 50% Concealment bonus against enemy attacks and can ignore the dexterity modifier of any opponent unless that opponent has the Uncanny dodge feat.
The ability to move about unseen is not foolproof. While they can’t be seen, invisible creatures can be heard.
Invisibility makes a creature undetectable by vision, including darkvision.
A creature can use hearing to find an invisible creature. A character can make a listen check for this purpose as a free action each round. A listen check result at least equal to the invisible creature’s move silently check result reveals its presence. (A creature with no ranks in move silently makes a move silently check as a dexterity check to which an armor check penalty applies.) A successful check lets a character hear an invisible creature "over there somewhere". It’s practically impossible to pinpoint the location of an invisible creature. A listen check that beats the DC by 20 pinpoints the invisible creature’s location.
Invisible creatures leave tracks. They can be tracked normally. Footprints in sand, mud, or other soft surfaces can give enemies clues to an invisible creature’s location.
An invisible creature in the water displaces water, revealing its location. The invisible creature, however, is still hard to see and benefits from concealment.
A creature with the Blind Fight feat has a better chance to hit an invisible creature. Roll the miss chance twice, and he misses only if both rolls indicate a miss. (Alternatively, make one 25% miss chance roll rather than two 50% miss chance rolls.)
Ethereal creatures are invisible. Since ethereal creatures are not materially present, Spot checks, listen checks, and Blind-Fight don’t help locate them. Incorporeal creatures are often invisible. Blind-Fight doesn’t help creatures find or attack invisible, incorporeal creatures, but Spot checks and possibly listen checks can help.
Invisibility does not thwart detect spells.
Since some creatures can detect or even see invisible creatures, it is helpful to be able to hide even when invisible.