Glue Traps can be effective for catching and trapping mice especially when the mice learn to avoid other traps such as the snap mouse trap.
You can lure the mouse to the glue trap by placing some food onto the glue trap and the mouse will then step onto the glue trap and then be stuck by the strong glue.
I prefer to use the snap traps because of the instant or near instant kill of the mouse but sometimes you get a mouse that avoids those traps and then I have to use the glue trap.
The glue trap doesn't kill the mouse but after a day or so the mouse will eventually die because they cannot get off.