Once I was asked to name what have learned about the world thanks to the field of topological phases that we didn’t know already from the quantum Hall effect. In this talk I will introduce, in the most intuitive way possible, what are topological phases, and why I think they are interesting. I will then introduce (as time permits) the research that we do in my group on three modern research directions: non-linear optical responses of topological phases, amorphous topological matter and out-of-equilibrium topological phases. These will act as (biased) examples of research directions we perhaps wouldn’t have guessed from the early days of the quantum Hall effect, the first topological phase.