This review will show that not all travel reviews are good reviews, but even bad experiences should be reported on.
On the day that we (a party of four) were supposed to leave, we decided to check and look on the Minneapolis/Saint Paul Airport website to see if Iceland Air Flight 656 from MSP to Reykjavik was on time or delayed. At that time, some in our party were already on their way to the airport.
To our surprise, we saw that there was no flight scheduled to Reykjavik from MSP and started calling Iceland Air in Maryland.
After calling back and forth for two and a half hours, we got put on the next day's flight to Reykjavik and we were all upgraded to business class for the flight over, but not the return flight. They said they would also try to upgrade our hotel. Also, they gave us all a free excursion in Iceland called "The Golden Circle Tour" and refunded us a night's stay at the Odinsve Hotel.
Iceland Air told us that there was never a flight planned that day and that we somehow fell through the cracks. Meanwhile, we were not the only ones they sold tickets to, as people were arriving at MSP airport only to find out that they were not going anywhere.
We left the next day and the rest of the trip went a lot better.