The grappling device is a device that straps to one's forearm (or other convenient place) and shoots out a cable that attaches to some place the user wants to get to, or in some cases to swing from.

In my opinion, the best way to go about doing this would be to use some sort of railgun or coilgun to fire out a projectile with a hook of some sort attached to it. The idea would then be to have it wrap around a pole a few times and then catch on itself, so the user could climb up the cable (possibly using hooks on the other hand) or swing from it.

Another approach would be to have the projectile simply attach itself to a surface. An extremely powerful electromagnet could be used, but this would require that the surface be ferromagnetic (metal) and the device be connected to an extremely powerful power source. A (slightly) more likely method would be to use a substance that solidifies on contact with the surface, sort of like spider webs. Research is being done on spider webs that will hopefully allow us to recreate an artificial "web" that does essentially the same thing.