Exotic manifolds are smooth manifolds which are homeomorphic but not diffeomorphic to each other. Constructing exotic manifolds in dimension four has been an active research area in low dimensional and symplectic topology over the last 30 years. In this talk, I will first remind the main concepts in geometric topology. Then, I will focus on dimension four, and discuss recent progress and major open problems in 4–manifolds theory. After going over some construction techniques, I will present our results, part of which are joint with A. Akhmedov, C. Karakurt, and D. Park.