Commas set off transitional words and phrases.

• Indeed, close coordination will be essential.
• Defeat may be inevitable; however, disgrace is not.
• The second report, on the other hand, shows a strong bias.

When such words and phrases fall in the middle of a clause, commas are sometimes unnecessary.

• They thus have no chips left to bargain with.
• The materials had indeed arrived.
• She would in fact see them that afternoon.

Commas set off parenthetical elements, such as authorial asides.

• All of us, to tell the truth, were completely amazed.
  
• It was, I should add, not the first time I'd seen him in this condition.