Professor Krum was also a dedicated supervisor of Honours and PhD students, and undertook the supervision of 24 PhD and 12 Honours students during his time at the University. He currently ranks first for the most citations and third for the highest number of publications from all Monash University researchers, in the 2010-2014 period. Over his career he published over 500 journal articles, 4 books and 22 book chapters.

He was a member of the Executive Committee that established the value of beta-blockers in severe heart failure. He was first author of a paper in the Journal of the American Medical Association that described for the first time, the finding that beta-blockers may produce an early beneficial effect on clinical outcomes rather than the previous paradigm that patients need to wait many months before observing any clear benefit from these therapies.