Pseudorandom subsets in number theory: recent results and open problems

In 2007 Dartyge and S\'{a}rk\"{o}zy introduced measures of pseudorandomness for subsets of $\{1,2,\cdots, N\}$.
Later many pseudorandom subsets were given and studied by using number theoretic methods. In this talk I will introduce the developments in this field, as well as several recent results in collaboration with Yanmei Cao, Mengyao Jing and Guotuo Zhang.