Foliations are useful geometric and dynamical objects. Topologically, their individual pieces (leaves) can be very complicated, but exhibit some broad structural features that might be described as strikingly simple. This talk will introduce some results of Ghys to this effect, and will take the opportunity to (attempt to) draw many examples, and mention connections to related topics such as infinite-type surfaces and certain aspects of geometric group theory. Speaker(s): Feng Zhu (University of Michigan)