Finite field models in arithmetic combinatorics – ten years on

It has been close to ten years since the publication of Green's influential survey Finite field models in additive combinatorics 28], in which the author championed the use of high-dimensional vector spaces over finite fields as a toy model for tackling additive problems concerning the integers. The path laid out by Green has proven to be a very successful one to follow. In the present article we survey the highlights of the past decade and outline the challenges for the years to come.