Penis enlargement surgery is also known as penile enhancement or penile augmentation. The surgery includes two types of procedures involved in the surgery. The first procedure involves increasing the thickness of the penis while the second procedure involves increasing the length of the penis. Most of the patients opt for both the procedures at the same time.
In case of increasing the base (or thickness) of the penis, the fat cells from the abdomen are transplanted around the penis. As a result the girth of the penis can be increased by about 2-3 inches. However a major drawback of this procedure is that the fat cells feel very soft and after sometime they may just get reabsorbed in the body. Many times the process is not regulated or even as a result of which the penis becomes lumpy and dull.
There is now an alternative procedure of fat transfer known as dermal transfer where strips of fat and skin are used together for transplantation. The skin does not let the fat get reabsorbed in the body. However this procedure of grafting the skin and fat around the penis is more complicated than the earlier procedures.
On the other hand penis lengthening procedures are more complicated than those procedures involved in increasing the thickness of the penis. The tissue by the name of corpora cavernosa is filled with blood during sexual stimulation. This tissue extends from the penis to the back of the body. In cases of erectile dysfunction, half of the tissue may get concealed in the body. Hence penis lengthening procedure involves cutting the suspensory ligaments that conceal the corpora cavernosa. As a result the concealed part of the penis is pushed outside the body. Hence this surgery can increase the flaccid size considerably but there is not much difference in the length of the penis.      
The biggest disadvantage of penis lengthening surgery is that your penis will seem to be floating loose as the suspensory ligament is no longer attached to the pubic bone. Hence during erection there can be some problems. The erect penis can shift and slip and even appear to face downwards. There are advance surgeries today that can solve this problem of angle to some extent. 
Today penis enlargement surgery has come a long way and gone are the days when there was no solution for penis related disorders. However many surgeons do not undertake penis enlargement procedures due to the risk associated with it. Hence it is best for patients to seek advice and counseling from their doctors before going in for surgical procedures.