There are currently three methods of hysterectomies performed by surgeons. These include:

Open hysterectomy : This type of uterus removal surgery involves an incision of size 6 to 12 centimeters in the abdominal wall.
Vaginal Hysterectomy : This involves removing the uterus through the vagina and was preferred over open hysterectomy. This method, however only allowed a limited view of the uterus for the surgeon.
Laparoscopic Hysterectomy : Using laparoscopes, the surgeon gets a full view of the surrounding organs and the procedure requires only small incisions. This can either be performed as a total laparoscopic procedure or as a laparoscopic assisted vaginal hysterectomy.
Laparoscopic Assisted Vaginal Hysterectomy : This is when a part of the removal is done with the laparoscope and the remaining is completed transvaginally.
Total Laparoscopic Hysterectomy : When the entire uterus removal surgery is performed using the laparoscope and the surgical specimen is removed through the vagina.

Supra cervical Hysterectomy : This is the removal of the upper part of the uterus just above the cervix.

Hysterectomy:
Removal of the uterus completely except the ovaries

Hysterectomy and bi lateral salpingo-Oophorectomy:
Complete removal of the uterus, fallopian tubes and the ovaries
This is known as a complete or pan – hysterectomy.

Less chance of infections
Less risk of vault prolapse
Lesser pain compared to open surgery.
Minimal blood loss.
Less scarring.
Shorter stay at the hospital.
A faster recovery to normal daily activities.

Although laparoscopic hysterectomy is a safe method, as with any surgical procedure there are chances of complications as well.

Bowel or bladder damage: There is a chance of accidental damage to nearby organs during the procedure.
Excessive Blood loss: This may occur during or after the procedure.
Infections: They're rare but sometimes infections may occur in the abdomen affecting the bladder, or in the lungs or at the site of surgical incisions.
Laparotomy: In cases where the surgeon cannot approach the uterus properly or when there is profuse bleeding then the procedure may have to be converted to open hysterectomy.