Monte Carlo event generators are the most widely used tools in collider particle physics. One of their core components is the parton shower, which connects the high momentum scales at which we seek to probe the Lagrangian of particle physics with the low momentum scales of the particles observed in experiments.

In this talk, I will discuss some of the progress made on parton showers in the past few years, addressing questions such as what a parton shower is supposed to achieve theoretically, how we can classify and improve the accuracy of these core tools, and the kinds of open issues that lie ahead of us.