One of the ones that work is called the 'Atkins Diet.' There is a book - The Dr Atkins Diet (~£7 from WH Smiths in the UK) - that explains it all. There is a lot of philosophical claims, but the diet works, losing about 2kg/wk.
My basic explanation is that the body uses 1 fuel only, glucose which it puts into the Krebs cycle and produces all the energy it needs. To get the glucose, it converts, in order: sugars, carbohydrates, fats then proteins. Don't give it the 1st 2 and it use the body's fat.
The diet boils down to any amount of meat, cheese, fish, eggs and butter (and cream/mayo!) you want plus a small plate of green salad, 4 oz off steamed veg per day and a vitamin tablet. It's not the most balanced of diets, but it works. Once I get down to my target weight, I revert to a more balanced, normal diet, but don't generally put it back on - christmas and holidays excepted.
I do bacon + eggs for b'fast, cheese + tuna mayo salad for lunch and meat veg and cheese for dinner.
It works, but best read the book.
Good luck!