1. In most cases, they provide very effective pain relief.
2. Most women can still push (I certainly could).
3. You can increase or decrease the rate of infusion according to your pain requirements, or ramp it right up if you need an episiotomy or instrument delivery at the end, which is often unforseeable.
4. It does not affect the baby, whereas drugs like pethidine can cause the baby's respiratory rate to fall quite low at birth, requiring intervention.
5. There have been studies which show epidurals do not prolong labour, which was a common previous misconception.
6. Maternal satisfaction is very high.
Of course, Button may disagree, and we need a counter point of view. One of the main complications of epidurals is not nerve damage (which people worry about), it is failure of the epidural to work, or a one-sided block (only half your tummy, not nice). The Anaesthetist can usually fix it by either pulling back the catheter, or repeating at a different spinal level (one level up usually). They don't hurt, other than the sting of the local anaesthetic injected into the skin before the epidural needle is inserted. Most patients tolerate them well. If you are having close contractions, you just need to warn the Anaesthetist each time so he/she can stop until the contraction is over. Takes about 15 minutes to reach peak effect, but after 8 hours of labour with my son, I wanted to hug the Anaesthetist!!
But, given my extensive experience in Anaesthesia, I am biased! So please ask Button too.