A lot has been said in favour of these types of diets in recent years. The evidence clearly supports its effectiveness in weight loss plans, as you enter a ketonic state; where instead of your body getting energy by burning carbs, it gets it from burning fat in your body instead.
While this makes sense, there are some health concerns for the diet, just as there are for the opposite; low protein and high carbohydrate diets. In high protein diets, there are large amounts of toxins released through the burning of fat, which can cause your kidneys to fail (although the chances of this are low). Whereas, in high carbohydrate diets, your body is deprived of protein, which it needs to be able to function well.
As with most things about keeping healthy, what it all comes down to is using as much energy as you’re absorbing through eating, and then otherwise making sure that you absorb all of the dietary requirements you need to be able to remain healthy.