  A covering system is a finite collection of arithmetic progressions whose
union is the set of integers. The study of these objects was initiated by
Erd\H{o}s in 1950, and over the following decades he asked many questions about
them. Most famously, he asked whether there exist covering systems with
distinct moduli whose minimum modulus is arbitrarily large. This problem was
resolved in 2015 by Hough, who showed that in any such system the minimum
modulus is at most $10^{16}$.
  The purpose of this note is to give a gentle exposition of a simpler and
stronger variant of Hough's method, which was recently used to answer several
other questions about covering systems. We hope that this technique, which we
call the distortion method, will have many further applications in other
combinatorial settings.
