This lecture serves as a background for the upcoming talk by Bharatram Rangarajan. I will review some aspects of bounded cohomology, including why it appears to have some relevance to stability questions. I will then explain vanishing results for the bounded cohomology of higher rank groups and their lattices. This includes results with Marc Burger, Yehuda Shalom, and time permitting a new variant of Borel-Serre vanishing based on a measurable Solomon-Tits theorem.