About the Paleolithic diet

The Paleolithic diet, also called paleo diet or Caveman diet, has ambiguous meaning:
from the point of view of palaeontological Sciences it intends to examine and document the human diet in the course of evolution of the species and over the geographic changes, behavioral and paleoclimatic
from the point of view of contemporary human diets intends to propose the kind of power that characterized the human populations who lived in the era preceding the discovery of agriculture, which occurred about 10,000 years ago.

For about two million years, humans drew sustenance from hunting, fishing and gathering of natural vegetation and meat; to support the Paleolithic diet is therefore the assumption that genetic and physiological level no man has undergone major changes since the Palaeolithic, although it is very evolved culturally, technological and scientific.
Consequently, the proper nutrition you should rely on foods that were available before the development of agricultural techniques, i.e. on "wild" products of all kinds, especially bone marrow, brains, offal, blood of mammals (the muscles of animals was consumed only if there was no other food), fish, crustaceans, reptiles, worms, bugs, insects, birds, eggs, berries, fruits, honey, newly sprouted plant, roots, bulbs, nuts, seeds, etc.
However, you should determine whether it is predominantly power collection and culinary preparation insects and reptiles (tropical South American Branch), Eskimo hunting and fishing or caterpillars, reptiles and bulbs of the Australian branch.
Here are the arguments of a fraction of this health movement (according to Dr. Loren Cordain).

What to eat

The paleodieta should eat foods that are as close as possible in their natural state: meat and offal, preferably wild or farmed animals without using grains; fish, again preferring caught fish, shellfish, crustaceans, molluscs, eggs, fruits and vegetables of all kinds, choice of seasonal products, moderate amount of dried fruit. The only permitted oil extra virgin olive oil. Of great importance are the fatty fish and mackerel, Bluefish, tuna, sardines, anchovies, halibut, because they contain significant amounts of omega-3 fatty acids.
As regards the percentages of macronutrients, they are not accurately fixed (as is so in other diets like for example in the Zone Diet) but provides a range: proteins are from 20% to 35% of calories from fat, 30% to 60% and 80% or more for some people, carbohydrates from 20% to 35% of calories. There are supporters, and among them also distinguished nutritionists such as Dr. Barry Groves of Paleolithic diets of meat and animal fat only; they are however very good for your health even after many years without carbohydrates. The percentages of macro-nutrients are magazines essentially for athletes depending on the circumstances and depending on the sport, but always in favor of carbohydrates. In these cases it is allowed to introduce foods preferably potatoes not Paleolithic (alkalizing) and, occasionally, wheat gluten, better digestible and low GI as basmati rice, though in line with the principles of the diet you can use honey instead of potatoes and cereals. Even the practice of sprouting grains and legumes, can be taken into account, in order to drastically reduce the anti-nutrients  in this case we don't talk more than seeds but of real vegetables, rich in starch and these fatty with a clearly downcast anti-nutrients  including especially the phytic acid, which tends to remove minerals from the intestinal lumen and cause serious deficiencies.

What not to eat

Everything that was not available in the old stone age and that is alien to the human genome, such as: cereals and their derivatives, legumes (including soy), milk and its derivatives. and to get rid of even tea, coffee, cocoa, wine, vinegar and salt. The reason for the removal of salt lies in the fact that to cover the body needs sodium contained in foods is adequate and adding more salt would result in a harmful imbalance between sodium and potassium.
Also corn oils and seeds and margarine should be removed from the diet: since these foods are rich in omega-6 fatty acids, which have inflammatory effect, the second because it consists of hydrogenated fats, very hazardous to your health.

Strengths

Following the Paleolithic model we introduce high dietary amounts of vitamins and co-factors vitamins, minerals, antioxidants, found in fruits, vegetables and meat.
In addition, the removal of seed oils and the habitual consumption of oily fish makes it possible to achieve the right balance between omega-3 fatty acids and omega-6, although it appears very difficult nowadays, given the difficulty to provide wild meat, get the ideal omega-3 and omega-6 without resorting to the use of supplements: it is estimated that in Paleolithic times the ratio was 1: 1.
The abundant consumption of vegetables and fruit and cereal and dairy exclusion brings benefits because the body produces an alkaline environment, with protective effects on bones and health in General.

Criticism

This diet is accused of being high in carbs; in fact, it does not restrict carbohydrates, and advises only to consume carbohydrates ingesting fruits and vegetables that are low GI and non-cereals and their derivatives.
Another criticism is the lack of calcium, given the exclusion of dairy products. It must be remembered in this regard such as dairy products, although rich in calcium, are very difficult to make and acidifying the assimilation of this mineral as well as altering the calcium/magnesium balance. In contrast, a diet rich in  alkalizing vegetables and fruits as paleo diet would have protective effect against osteoporosis.
A final objection claims that over time it is possible that there have been changes with respect to the human gene pool, so the man would be adapted to the consumption of dairy products and/or cereal.