Icelandair’s user friendly website allows you to purchase and book seats with a minimum of aggravation. They fly only one nonstop each day from Reykjavik to Munich, departing at 7:20a, arriving at 1:05p. All other flights make a stop. Grudgingly flying Icelandair, a non-Star Alliance partner, I must admit it is a very nice carrier, and they offer free stopovers when booking with them. Plan a stopover on your way to or from Europe for up to seven nights in either direction.
Icelandair flies nonstop to Reykjavik year-round from Boston, New York, Seattle, Denver and seasonal service from other cities and I think they are adding service to Chicago. Two women from New York on the L’Austral Iceland Cruise took advantage of this offer and flew to London for a four-night stay and then on to Reykjavik at no extra cost. Such a deal!