Determining the size of a largest subset of Fn3F3n which contains no lines is called the cap set problem. I will outline what is known about this problem and report some recent progress on the asymptotic version of the problem, due to Croot, Lev, Pach and Ellenberg, Gijswijt. Croot, E. , Lev, V. F. , Pach, P. P. Progression-free sets in Zn4Z4n are exponentially small, Annals of Math. 185, (2017), 331---337. Ellenberg, J. , Gijswijt, D. On large subsets of FnqFqn with no three-term arithmetic progression, Annals of Math. 185, (2017), 339---343