Hessenberg varieties are subvarieties of a full flag variety. Their topology makes connections with other research areas such as hyperplane arrangements and graph theory. In this talk, first I explain an explicit presentation of the cohomology rings of regular nilpotent Hessenberg varieties in type A which is joint work with Hiraku Abe, Megumi Harada, and Mikiya Masuda. Then, I would like to explain that their cohomology rings can be described in terms of hyperplane arrangements which is joint work with Takuro Abe, Mikiya Masuda, Satoshi Murai, and Takashi Sato. Finally, if I have time, then I would like to explain an explicit presentation of the cohomology rings of regular nilpotent Hessenberg varieties in all Lie types from the point of view of hyperplane arrangements which is joint work with Makoto Enokizono, Takahiro Nagaoka, and Akiyoshi Tsuchiya.