The UEFA Champions League reaches the second round of qualifying, with Celtic and Steaua Bucharest among those joining the competition.
Ronny Deila believes Celtic are a different proposition to team that failed to make the UEFA Champions League group stages 12 months ago, as they prepare to enter the second round of qualifiers against Stjarnan.
The Scottish champions were knocked out in the third round of qualifiers by Legia Warsaw last season, only to be handed a second chance when the Polish side were disqualified for fielding an ineligible player.
Celtic failed to make the most of the reprieve, though, and were beaten in the play-off round by Slovenian side Maribor.
Deila had not been in Glasgow long at that point, having replaced former boss Neil Lennon, and the Norwegian admits that he may have made mistakes early in his Celtic career that he hopes to avoid this time around.
"Maybe I wish I'd done some things differently. But at that time, there were a lot of new things for me to deal with," he said ahead of Wednesday's first leg versus the Icelandic side at Celtic Park.
"There was a big transition, but we're in a much better place now than we were one year ago. When I think back, we just weren't good enough. So it doesn't irritate me too much.
"Everyone at this club is doing everything they can, every day, to prepare for these qualifying games. I now really believe that we're good enough."
Wednesday also sees the Swedish and Croatian champions in action, as Malmo and Dinamo Zagreb host Zalgiris and Fola respectively, while Dundalk and Rudar Pljevlja have away ties with BATE and Qarabag.
On Tuesday, Steaua Bucharest - winner of Europe's premier competition in 1986 - look to overcome a sloppy start to their domestic season away to Slovakian side Trencin in Zilina.
Steaua completed a domestic treble in Romania last term, but head coach Constantin Galca and several first-team players including captain Cristian Tanase left in the close-season.
Mirel Radoi subsequently took the top job and has overseen a 1-0 defeat to Targu Mures in the Romanian Super Cup and a 0-0 draw with Petrolul Ploiesti in their Liga 1 opener.
Radoi, who enjoyed eight years as a player at Steaua, will be unable to take charge of the team against Trencin, though, as he does not have the necessary badges to coach in Europe. Massimo Pedrazzini will therefore take official control of team affairs.
Lincoln Red Imps became the first team from Gibraltar to win a Champions League tie when they beat Santa Coloma to reach the second round of qualifying. They journey continues with a trip to Denmark to face Midtjylland.
The New Saints, Crusaders and Pyunik also came through first-round qualifiers, and will play Videoton, Skenderbeu and Molde respectively.
Elsewhere, Ludogorets - who made the group stages last term - host Milsami, while Ventspils and APOEL are at home to HJK and Vardar. Maccabi Tel Aviv, Astana, Dila and Lech Poznan face respective trips to Hibernians, Maribor, Partizan and Sarajevo.