Simple Lie groups and simple algebraic groups over local fields are the most prominent members of the class S of compactly generated non-discrete simple locally compact groups. We outline a new trend, which emerged in the past decade, whose purpose is the study of S as a whole.
Caprace, P.-E. (2018). Non-discrete simple locally compact groups. In Caprace, Pierre-Emmanuel (ed.), European Congress of Mathematics (p. p. 333–354). Volker Mehrmann, Martin Skutella. https://doi.org/10.4171/176-1/15