At university we would put some bread in an empty milk bottle and tilt it against the wall in a corner. Mouse climbs in but can't get out. Then you can either release it in your neighbour's garden or fill the bottle with water and leave the room.
That post turned unexpectedly dark at the end! Just as well I wasn't taking a mouthful of coffee when I read it, as I had been moments earlier.
Fwiw, I don't think there's anything humane about letting them live. Old-skool snap traps are the best option, although as noted they sometimes don't do the job - I was woken one night by strange noises coming from behind the kitchen cupboards, which turned out to be a mouse trying to drag its broken body back into its hole with trap attached. On another occasion, I found a dismembered leg in a trap, the owner of which had made like James Franco in 127 Hours. I don't find that kind of thing amusing or entertaining but I don't lose any sleep over it either - it's only a mouse, FFS. And it's no worse than releasing them into the wild, which is not a kindness, it's misguided sentimentality. They will only starve, freeze or get eaten.