Summary: The existence of fixed points for pointwise eventually non-expansive mappings in modular spaces is proved. The results given by M. Bachar et al. [Math. Nachr. 292, No. 9, 1931–1940 (2019; Zbl 1482.46012)] and B. A. B. Dehaish and M. A. Khamsi [J. Nonlinear Sci. Appl. 9, No. 8, 5219–5228 (2016; Zbl 1477.47050)] are improved. Finally, the results of the article partially answers an open problem raised by W. A. Kirk and H.-K. Xu [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4706–4712 (2008; Zbl 1172.47038)] in the setting of modular spaces.