Layered rhenium dichalcogenides, represented by ReS2 and ReSe2, have recently emerged as rising-star two-dimensional (2D) materials with a distorted 1 T structure. Due to their low in-plane crystal symmetry in comparison with popular 2D semiconductors (e.g., MoS2, MoSe2, WS2, and WSe2), rhenium dichalcogenides exhibit unique anisotropy in electrical, thermal, and optical properties. In particular, strongly anisotropic excitons in rhenium dichalcogenides provide intriguing photophysics that are of both scientific and practical interest. In this mini-review, we discuss the fundamental properties of the anisotropic excitons in 2D rhenium dichalcogenides. First, we introduce basic atomic and electronic structures of rhenium dichalcogenides and their thickness dependence. Next, we discuss details of characteristics of the anisotropic excitons, including polarization selectivity, ultrafast dynamics, coherent light-matter interactions, and optical nonlinearity. We also cover cutting-edge findings on new features of the anisotropic excitons in rhenium dichalcogenides. This mini-review ends with challenges and an outlook of 2D rhenium dichalcogenides physics.