In the UK, they were massive. Take On Me wasn't their biggest hit here (it reached number two). The Sun Always Shines on TV reached number one. Then there were other top ten singles - Cry Wolf, Train of Thought, Hunting High and Low (particularly great in the single version), The Living Daylights (I prefer the album version to the version that appeared in the film), Stay on these Roads, Manhattan Skyline, Touchy, You Are the One, The Blood That Moves the Body, and my personal favourite, I've Been Losing You. My favourite album is Scoundrel Days (their second), which has some stunners that really should have been singles as well (especially the title song).
And of course, that's just the 1980s.