There is heaps of (mis)information about the biggest carp ever caught, but it seems to me the world record carp was caught by Graham Slaughter (what a great name!!) of Britain. His carp weighed in at a whopping 88.6lbs and is believed to be the only carp caught over 40 kilos in the world. To put that into perspective the women Chinese Olympic divers weigh in at around 37 kilos!
Here is a picture of the world record fish (click to enlarge)

It is an amazing fish and I have never seen anything like it. It looks like it has been seriously pigging out on anglers baits for years and years without doing any exercise!
Here is a video of the previous world record carp, which weighed in at 87lb 2oz and although it isn't 40kg it is still a great fish. The video is well worth a watch if you like giant carp!