Triumph are arguably one of Canada's greatest rock bands, there's not many who would argue with that.  

The trio was sometimes overshadowed by Rush, but the bands really were quite different.  Triumph had some progressive tendencies, but nothing like Rush.  Triumph was more on the AOR side and wasn't afraid to write a song just for the sake of something that would fit the arenas.  They also had a larger female base than Rush did at the time.

Unfortunately their music became a bit dated in the 90's and they stick together, but their early material will forever be remembered as some of the most powerful and beautiful rock ever written.  They did have an influence on Metal too, Rik Emmett's guitar-work was as powerful as his voice and many bands from the 80's have to thank Triumph for paving the way.